YES 207.604 H-Termination proof of /home/matraf/haskell/eval_FullyBlown_Fast/FiniteMap.hs
H-Termination of the given Haskell-Program with start terms could successfully be proven:



↳ HASKELL
  ↳ LR

mainModule FiniteMap
  ((intersectFM_C :: (a  ->  c  ->  b)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering c  ->  FiniteMap Ordering b) :: (a  ->  c  ->  b)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering c  ->  FiniteMap Ordering b)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

  sizeFM :: FiniteMap 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 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



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

is transformed to
mid_key10 (mid_key1,_) = mid_key1

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

is transformed to
mid_elt10 (_,mid_elt1) = mid_elt1

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

is transformed to
mid_key20 (mid_key2,_) = mid_key2

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

is transformed to
mid_elt20 (_,mid_elt2) = mid_elt2

The following Lambda expression
\(Just elt1)→elt1

is transformed to
elt10 (Just elt1) = elt1

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

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

The following Lambda expression
\oldnew→new

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

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

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

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

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


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



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

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

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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((intersectFM_C :: (b  ->  c  ->  a)  ->  FiniteMap Ordering b  ->  FiniteMap Ordering c  ->  FiniteMap Ordering a) :: (b  ->  c  ->  a)  ->  FiniteMap Ordering b  ->  FiniteMap Ordering c  ->  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 b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


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



If Reductions:
The following If expression
if primGEqNatS x y then Succ (primDivNatS (primMinusNatS x y) (Succ y)) else Zero

is transformed to
primDivNatS0 x y True = Succ (primDivNatS (primMinusNatS x y) (Succ y))
primDivNatS0 x y False = Zero

The following If expression
if primGEqNatS x y then primModNatS (primMinusNatS x y) (Succ y) else Succ x

is transformed to
primModNatS0 x y True = primModNatS (primMinusNatS x y) (Succ y)
primModNatS0 x y False = Succ x



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

mainModule FiniteMap
  ((intersectFM_C :: (c  ->  a  ->  b)  ->  FiniteMap Ordering c  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b) :: (c  ->  a  ->  b)  ->  FiniteMap Ordering c  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b)

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

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

  
addToFM0 old new = new

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

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

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

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

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

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


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



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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((intersectFM_C :: (a  ->  c  ->  b)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering c  ->  FiniteMap Ordering b) :: (a  ->  c  ->  b)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering c  ->  FiniteMap Ordering b)

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

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

  
addToFM0 old new = new

  addToFM_C :: Ord 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 vwx fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwy fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

  mkBalBranch :: Ord 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 vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) 
 | sizeFM fm_rl < 2 * sizeFM fm_rr = 
single_L fm_L fm_R
 | otherwise = 
double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) 
 | sizeFM fm_lr < 2 * sizeFM fm_ll = 
single_R fm_L fm_R
 | otherwise = 
double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l = sizeFM fm_L
size_r = sizeFM fm_R

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

  mkVBalBranch :: Ord b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
 | otherwise = 
mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) where 
size_l = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r = sizeFM (Branch vvy vvz vwu vwv vww)

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


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



Cond Reductions:
The following Function with conditions
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt xx fm_l fm_r) split_key
 | split_key < key
 = splitLT fm_l split_key
 | split_key > key
 = mkVBalBranch key elt fm_l (splitLT fm_r split_key)
 | otherwise
 = fm_l

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

splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

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

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

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

splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 xux xuy = splitGT3 xux xuy

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

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

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

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

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

The following Function with conditions
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
 | sIZE_RATIO * size_l < size_r
 = mkBalBranch vvy vvz (mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) vwv) vww
 | sIZE_RATIO * size_r < size_l
 = mkBalBranch vuy vuz vvv (mkVBalBranch key elt vvw (Branch vvy vvz vwu vwv vww))
 | otherwise
 = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)
where 
size_l  = sizeFM (Branch vuy vuz vvu vvv vvw)
size_r  = sizeFM (Branch vvy vvz vwu vwv vww)

is transformed to
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

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

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

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

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R

is transformed to
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)

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

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

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

The following Function with conditions
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R

is transformed to
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)

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

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

mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

The following Function with conditions
mkBalBranch key elt fm_L fm_R
 | size_l + size_r < 2
 = mkBranch 1 key elt fm_L fm_R
 | size_r > sIZE_RATIO * size_l
 = mkBalBranch0 fm_L fm_R fm_R
 | size_l > sIZE_RATIO * size_r
 = mkBalBranch1 fm_L fm_R fm_L
 | otherwise
 = mkBranch 2 key elt fm_L fm_R
where 
double_L fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
 | sizeFM fm_rl < 2 * sizeFM fm_rr
 = single_L fm_L fm_R
 | otherwise
 = double_L fm_L fm_R
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
 | sizeFM fm_lr < 2 * sizeFM fm_ll
 = single_R fm_L fm_R
 | otherwise
 = double_R fm_L fm_R
single_L fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

is transformed to
mkBalBranch key elt fm_L fm_R = mkBalBranch6 key elt fm_L fm_R

mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

The following Function with conditions
addToFM_C combiner EmptyFM key elt = unitFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt
 | new_key < key
 = mkBalBranch key elt (addToFM_C combiner fm_l new_key new_elt) fm_r
 | new_key > key
 = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
 | otherwise
 = Branch new_key (combiner elt new_elt) size fm_l fm_r

is transformed to
addToFM_C combiner EmptyFM key elt = addToFM_C4 combiner EmptyFM key elt
addToFM_C combiner (Branch key elt size fm_l fm_r) new_key new_elt = addToFM_C3 combiner (Branch key elt size fm_l fm_r) new_key new_elt

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

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

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

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

addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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

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

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

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

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

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

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

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

lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

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

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

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

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

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

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

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

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

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

is transformed to
compare x y = compare3 x y

compare0 x y True = GT

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

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

compare3 x y = compare2 x y (x == y)

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

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

gcd'0 x y = gcd' y (x `rem` y)

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

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

The following Function with conditions
gcd 0 0 = error []
gcd x y = 
gcd' (abs x) (abs y)
where 
gcd' x 0 = x
gcd' x y = gcd' y (x `rem` y)

is transformed to
gcd yxy yxz = gcd3 yxy yxz
gcd x y = gcd0 x y

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

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

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

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

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

is transformed to
absReal x = absReal2 x

absReal0 x True = `negate` x

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

absReal2 x = absReal1 x (x >= 0)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False

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

is transformed to
reduce x y = reduce2 x y

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



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

mainModule FiniteMap
  ((intersectFM_C :: (a  ->  b  ->  c)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b  ->  FiniteMap Ordering c) :: (a  ->  b  ->  c)  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b  ->  FiniteMap Ordering c)

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

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

  glueBal :: Ord 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 (vzx,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (vzy,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,vzz) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,wuu) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

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

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

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

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

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

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

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

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

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

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

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

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

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

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

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

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

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

  
mkBalBranch6 key elt fm_L fm_R = 
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2) where 
double_L fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l = sizeFM fm_L
size_r = sizeFM fm_R

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xux xuy = splitGT3 xux xuy

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

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


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



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

are unpacked to the following functions on top level
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

intersectFM_C2Gts yzw yzx = splitGT yzw yzx

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

intersectFM_C2Lts yzw yzx = splitLT yzw yzx

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

intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

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

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

are unpacked to the following functions on top level
glueBal2Vv3 yzy yzz = findMin yzy

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

glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

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

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_key1 yzy yzz = glueBal2Mid_key10 yzy yzz (glueBal2Vv2 yzy yzz)

glueBal2Vv2 yzy yzz = findMax yzz

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

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

glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

The bindings of the following Let/Where expression
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r vxz (Branch key_rl elt_rl vyu fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 key elt fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)
double_R (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 key elt fm_lrr fm_r)
mkBalBranch0 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyv vyw vyx fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyv vyw vyx fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyv vyw vyx fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vxw vxx vxy fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)
mkBalBranch2 key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R
mkBalBranch3 key elt fm_L fm_R True = mkBalBranch1 fm_L fm_R fm_L
mkBalBranch3 key elt fm_L fm_R False = mkBalBranch2 key elt fm_L fm_R otherwise
mkBalBranch4 key elt fm_L fm_R True = mkBalBranch0 fm_L fm_R fm_R
mkBalBranch4 key elt fm_L fm_R False = mkBalBranch3 key elt fm_L fm_R (size_l > sIZE_RATIO * size_r)
mkBalBranch5 key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch5 key elt fm_L fm_R False = mkBalBranch4 key elt fm_L fm_R (size_r > sIZE_RATIO * size_l)
single_L fm_l (Branch key_r elt_r vyy fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 key elt fm_l fm_rl) fm_rr
single_R (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

are unpacked to the following functions on top level
mkBalBranch6MkBalBranch12 zuu zuv zuw zux fm_L fm_R (Branch vxw vxx vxy fm_ll fm_lr) = mkBalBranch6MkBalBranch11 zuu zuv zuw zux fm_L fm_R vxw vxx vxy fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

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

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

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

mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

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

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

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

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

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

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

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

mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

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

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

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

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

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

are unpacked to the following functions on top level
glueVBal3GlueVBal0 zuy zuz zvu zvv zvw zvx zvy zvz zwu zwv yy yz zu zv zw zy zz vuu vuv vuw True = glueBal (Branch yy yz zu zv zw) (Branch zy zz vuu vuv vuw)

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

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

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

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

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

are unpacked to the following functions on top level
mkBranchBalance_ok zww zwx zwy = True

mkBranchRight_size zww zwx zwy = sizeFM zww

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

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

mkBranchUnbox zww zwx zwy x = x

mkBranchLeft_size zww zwx zwy = sizeFM zwy

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

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

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 zwz zxw (1 + mkBranchLeft_size zxv zwz zxw + mkBranchRight_size zxv zwz zxw)) zxw zxv

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

are unpacked to the following functions on top level
mkVBalBranch3MkVBalBranch0 zxx zxy zxz zyu zyv zyw zyx zyy zyz zzu key elt vuy vuz vvu vvv vvw vvy vvz vwu vwv vww True = mkBranch 13 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

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

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

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

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

The bindings of the following Let/Where expression
let 
biggest_left_key  = fst (findMax fm_l)
in biggest_left_key < key

are unpacked to the following functions on top level
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

The bindings of the following Let/Where expression
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key

are unpacked to the following functions on top level
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

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

are unpacked to the following functions on top level
reduce2Reduce1 zzx zzy x y True = error []
reduce2Reduce1 zzx zzy x y False = reduce2Reduce0 zzx zzy x y otherwise

reduce2D zzx zzy = gcd zzx zzy

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

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

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

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

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

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



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

mainModule FiniteMap
  ((intersectFM_C :: (c  ->  a  ->  b)  ->  FiniteMap Ordering c  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b) :: (c  ->  a  ->  b)  ->  FiniteMap Ordering c  ->  FiniteMap Ordering a  ->  FiniteMap Ordering b)

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

  addToFM :: Ord 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 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

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

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

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

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

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

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

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

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

  
glueBal2Mid_elt10 yzy yzz (vzx,mid_elt1) = mid_elt1

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

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

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

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

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

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzz

  
glueBal2Vv3 yzy yzz = findMin yzy

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

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

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

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

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

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

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

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

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

  
mkBranchBalance_ok zww zwx zwy = True

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

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

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwy

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

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

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

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xux xuy = splitGT3 xux xuy

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

  unitFM :: 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_C :: (b  ->  a  ->  c)  ->  FiniteMap Ordering b  ->  FiniteMap Ordering a  ->  FiniteMap Ordering c)

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

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

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xyz xzu xzv xzw = addToFM_C3 xyz xzu xzv xzw

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

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

  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 (vzx,mid_elt1) = mid_elt1

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

  
glueBal2Mid_elt20 yzy yzz (vzy,mid_elt2) = mid_elt2

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

  
glueBal2Mid_key10 yzy yzz (mid_key1,vzz) = mid_key1

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

  
glueBal2Mid_key20 yzy yzz (mid_key2,wuu) = mid_key2

  
glueBal2Vv2 yzy yzz = findMax yzz

  
glueBal2Vv3 yzy yzz = findMin yzy

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  
intersectFM_C2Elt10 yzw yzx (Just elt1) = elt1

  
intersectFM_C2Gts yzw yzx = splitGT yzw yzx

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

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

  
intersectFM_C2Lts yzw yzx = splitLT yzw yzx

  
intersectFM_C2Maybe_elt1 yzw yzx = lookupFM yzw yzx

  
intersectFM_C2Vv1 yzw yzx = intersectFM_C2Maybe_elt1 yzw yzx

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

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

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

  
lookupFM0 key elt wuv fm_l fm_r key_to_find True = Just elt

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

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

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

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

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

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

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

  
mkBalBranch6Double_R zuu zuv zuw zux (Branch key_l elt_l vxu fm_ll (Branch key_lr elt_lr vxv fm_lrl fm_lrr)) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))) key_lr elt_lr (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))) key_l elt_l fm_ll fm_lrl) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))))))) zuu zuv fm_lrr fm_r)

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

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

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

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

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

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

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

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

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

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

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

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

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

  
mkBalBranch6Single_R zuu zuv zuw zux (Branch key_l elt_l vwz fm_ll fm_lr) fm_r = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero))))))))) key_l elt_l fm_ll (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))) zuu zuv fm_lr fm_r)

  
mkBalBranch6Size_l zuu zuv zuw zux = sizeFM zuw

  
mkBalBranch6Size_r zuu zuv zuw zux = sizeFM zux

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

  
mkBranchBalance_ok zww zwx zwy = True

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

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

  
mkBranchLeft_ok0Biggest_left_key zzv = fst (findMax zzv)

  
mkBranchLeft_size zww zwx zwy = sizeFM zwy

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

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

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

  
mkBranchRight_ok0Smallest_right_key zzw = fst (findMin zzw)

  
mkBranchRight_size zww zwx zwy = sizeFM zww

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

  mkVBalBranch :: Ord a => a  ->  b  ->  FiniteMap a b  ->  FiniteMap a b  ->  FiniteMap a b
mkVBalBranch key elt EmptyFM fm_r = mkVBalBranch5 key elt EmptyFM fm_r
mkVBalBranch key elt fm_l EmptyFM = mkVBalBranch4 key elt fm_l EmptyFM
mkVBalBranch key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww) = mkVBalBranch3 key elt (Branch vuy vuz vvu vvv vvw) (Branch vvy vvz vwu vwv vww)

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

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

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

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

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

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

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

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

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

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

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

  
splitGT0 key elt xy fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 xux xuy = splitGT3 xux xuy

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

  
splitLT0 key elt xx fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wzz xuu = splitLT3 wzz xuu

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


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



Haskell To QDPs


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

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

new_intersectFM_C2Elt100(zzz2045, EQ, zzz2047, zzz2048, zzz2049, zzz2050, h) → new_intersectFM_C2Elt10(zzz2045, zzz2050, h)
new_intersectFM_C2Elt100(zzz2045, LT, zzz2047, zzz2048, zzz2049, Branch(zzz20500, zzz20501, zzz20502, zzz20503, zzz20504), h) → new_intersectFM_C2Elt100(zzz2045, zzz20500, zzz20501, zzz20502, zzz20503, zzz20504, h)
new_intersectFM_C2Elt10(zzz2045, Branch(zzz20500, zzz20501, zzz20502, zzz20503, zzz20504), h) → new_intersectFM_C2Elt100(zzz2045, zzz20500, zzz20501, zzz20502, zzz20503, zzz20504, 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
                                    ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_intersectFM_C2Elt101(zzz2018, zzz2019, zzz2020, zzz2021, Branch(zzz20250, zzz20251, zzz20252, zzz20253, zzz20254), h) → new_intersectFM_C2Elt102(zzz2018, zzz2019, zzz2020, zzz2021, zzz20250, zzz20251, zzz20252, zzz20253, zzz20254, h)
new_intersectFM_C2Elt102(zzz2018, zzz2019, zzz2020, zzz2021, GT, zzz2023, zzz2024, Branch(zzz20250, zzz20251, zzz20252, zzz20253, zzz20254), zzz2026, h) → new_intersectFM_C2Elt102(zzz2018, zzz2019, zzz2020, zzz2021, zzz20250, zzz20251, zzz20252, zzz20253, zzz20254, h)
new_intersectFM_C2Elt102(zzz2018, zzz2019, zzz2020, zzz2021, LT, zzz2023, zzz2024, zzz2025, zzz2026, h) → new_intersectFM_C2Elt101(zzz2018, zzz2019, zzz2020, zzz2021, zzz2026, 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
                                    ↳ 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
                                  ↳ QDP
                                  ↳ QDP

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

new_intersectFM_C2Elt104(zzz1979, zzz1980, zzz1981, zzz1982, GT, zzz1984, zzz1985, Branch(zzz19860, zzz19861, zzz19862, zzz19863, zzz19864), zzz1987, h) → new_intersectFM_C2Elt104(zzz1979, zzz1980, zzz1981, zzz1982, zzz19860, zzz19861, zzz19862, zzz19863, zzz19864, h)
new_intersectFM_C2Elt104(zzz1979, zzz1980, zzz1981, zzz1982, LT, zzz1984, zzz1985, zzz1986, zzz1987, h) → new_intersectFM_C2Elt103(zzz1979, zzz1980, zzz1981, zzz1982, zzz1987, h)
new_intersectFM_C2Elt103(zzz1979, zzz1980, zzz1981, zzz1982, Branch(zzz19860, zzz19861, zzz19862, zzz19863, zzz19864), h) → new_intersectFM_C2Elt104(zzz1979, zzz1980, zzz1981, zzz1982, zzz19860, zzz19861, zzz19862, zzz19863, zzz19864, 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
                                    ↳ 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
                                  ↳ QDP

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

new_glueBal2Mid_key10(zzz1944, zzz1945, zzz1946, zzz1947, zzz1948, zzz1949, zzz1950, zzz1951, zzz1952, zzz1953, zzz1954, zzz1955, zzz1956, zzz1957, Branch(zzz19580, zzz19581, zzz19582, zzz19583, zzz19584), h, ba) → new_glueBal2Mid_key10(zzz1944, zzz1945, zzz1946, zzz1947, zzz1948, zzz1949, zzz1950, zzz1951, zzz1952, zzz1953, zzz19580, zzz19581, zzz19582, zzz19583, zzz19584, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_glueBal2Mid_elt10(zzz1928, zzz1929, zzz1930, zzz1931, zzz1932, zzz1933, zzz1934, zzz1935, zzz1936, zzz1937, zzz1938, zzz1939, zzz1940, zzz1941, Branch(zzz19420, zzz19421, zzz19422, zzz19423, zzz19424), h, ba) → new_glueBal2Mid_elt10(zzz1928, zzz1929, zzz1930, zzz1931, zzz1932, zzz1933, zzz1934, zzz1935, zzz1936, zzz1937, zzz19420, zzz19421, zzz19422, zzz19423, zzz19424, 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
                                    ↳ 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_key20(zzz1912, zzz1913, zzz1914, zzz1915, zzz1916, zzz1917, zzz1918, zzz1919, zzz1920, zzz1921, zzz1922, zzz1923, zzz1924, Branch(zzz19250, zzz19251, zzz19252, zzz19253, zzz19254), zzz1926, h, ba) → new_glueBal2Mid_key20(zzz1912, zzz1913, zzz1914, zzz1915, zzz1916, zzz1917, zzz1918, zzz1919, zzz1920, zzz1921, zzz19250, zzz19251, zzz19252, zzz19253, zzz19254, 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
                                    ↳ 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(zzz1896, zzz1897, zzz1898, zzz1899, zzz1900, zzz1901, zzz1902, zzz1903, zzz1904, zzz1905, zzz1906, zzz1907, zzz1908, Branch(zzz19090, zzz19091, zzz19092, zzz19093, zzz19094), zzz1910, h, ba) → new_glueBal2Mid_elt20(zzz1896, zzz1897, zzz1898, zzz1899, zzz1900, zzz1901, zzz1902, zzz1903, zzz1904, zzz1905, zzz19090, zzz19091, zzz19092, zzz19093, zzz19094, h, ba)

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

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



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

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

new_intersectFM_C2Elt105(zzz1963, Branch(GT, zzz19641, zzz19642, zzz19643, zzz19644), h) → new_intersectFM_C2Elt105(zzz1963, zzz19643, h)
new_intersectFM_C2Elt105(zzz1963, Branch(EQ, zzz19641, zzz19642, zzz19643, zzz19644), h) → new_intersectFM_C2Elt105(zzz1963, zzz19643, 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
                                    ↳ 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(zzz72000)) → new_primPlusNat(zzz72000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primMinusNat(Succ(zzz94600), Succ(zzz642000)) → new_primMinusNat(zzz94600, zzz642000)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_primPlusNat0(Succ(zzz940), Succ(zzz9500)) → new_primPlusNat0(zzz940, zzz9500)

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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch11(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Succ(zzz203500), h, ba) → new_mkBalBranch6MkBalBranch11(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2027000, zzz203500, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch3(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Succ(zzz200300), h, ba) → new_mkBalBranch6MkBalBranch3(zzz147530, zzz147531, zzz1836, zzz147534, zzz1988000, zzz200300, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkBalBranch6MkBalBranch01(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Succ(zzz201500), h, ba) → new_mkBalBranch6MkBalBranch01(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz1990000, zzz201500, 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
                                    ↳ 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(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Succ(zzz196500), h, ba) → new_mkBalBranch6MkBalBranch4(zzz147530, zzz147531, zzz1836, zzz147534, zzz1961000, zzz196500, 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
                                  ↳ 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(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), h, ba) → new_deleteMax(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, 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
                                  ↳ 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(zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, h, ba) → new_deleteMin(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, 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
                                  ↳ 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(zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, Succ(zzz1818000), Succ(zzz1817000), h, ba) → new_glueBal2GlueBal1(zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1818000, zzz1817000, 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
                                  ↳ 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(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17410, h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174900), zzz17820, h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174900, zzz17820, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, Zero, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal16(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174900, Zero, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Neg(zzz17080), h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17820, h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal16(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz178100), Succ(Succ(zzz1749000)), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz178100), Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz170800, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174900, zzz17820, h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Succ(Succ(zzz1708000)), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Succ(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz170800), zzz17410, h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, zzz17410, h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(Succ(zzz1708000)), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal16(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(Succ(zzz1749000)), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1749, h, ba) → new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1749, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1708, h, ba) → new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1708, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Pos(zzz17490), h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz178100)), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, zzz17410, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, Succ(zzz17410), Pos(zzz17080), h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz17400, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz174900, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz147530, zzz147531, zzz147532, zzz147533, zzz147534), h, ba)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714), h, ba)
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), bb, bc) → zzz13792

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(Zero, Zero)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat1(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 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
                                    ↳ 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(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17410, h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1749, h, ba) → new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1749, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1708, h, ba) → new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1708, h, ba)
new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, Zero, h, ba)
new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17820, h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Neg(zzz17080), h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz178100), Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz170800, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Pos(zzz17490), h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174900, zzz17820, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz178100)), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, zzz17410, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, Succ(zzz17410), Pos(zzz17080), h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz17400, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz174900, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz147530, zzz147531, zzz147532, zzz147533, zzz147534), h, ba)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714), h, ba)
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), bb, bc) → zzz13792

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(Zero, Zero)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat1(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
                                    ↳ 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(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17410, h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Succ(zzz1708000))), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz174000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1749, h, ba) → new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1749, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174000, zzz1708000, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1708000), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz1708, h, ba) → new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), zzz1708, h, ba)
new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, Zero, h, ba)
new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz17820, h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Neg(zzz17080), h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz178100), Succ(zzz1749000), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal25(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal27(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz170800, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, Branch(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144), zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Pos(zzz17490), h, ba) → new_glueVBal3(zzz147140, zzz147141, zzz147142, zzz147143, zzz147144, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz174900, zzz17820, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17820), Neg(Zero), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17400), Pos(Zero), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal14(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz174000), Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Succ(zzz178100)), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal1(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz178100, zzz1749000, h, ba)
new_glueVBal3GlueVBal12(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Pos(zzz17780), zzz1749, h, ba) → new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17780), zzz1749, h, ba)
new_glueVBal3GlueVBal28(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_glueVBal3GlueVBal11(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba), h, ba)
new_glueVBal3GlueVBal20(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Neg(zzz17370), zzz1708, h, ba) → new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, new_primMulNat(zzz17370), zzz1708, h, ba)
new_glueVBal3GlueVBal21(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(zzz17410), Neg(Succ(zzz170800)), h, ba) → new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz170800, zzz17410, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Succ(Zero), Pos(Succ(Succ(zzz1749000))), h, ba) → new_glueVBal3GlueVBal10(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal22(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, Branch(zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334), zzz147534, Succ(zzz17410), Pos(zzz17080), h, ba) → new_glueVBal3GlueVBal2(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz1475330, zzz1475331, zzz1475332, zzz1475333, zzz1475334, h, ba), h, ba)
new_glueVBal3GlueVBal29(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, zzz17400, Zero, h, ba) → new_glueVBal3GlueVBal24(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)
new_glueVBal3GlueVBal13(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Pos(Succ(zzz174900)), h, ba) → new_glueVBal3GlueVBal15(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, zzz174900, h, ba)
new_glueVBal3GlueVBal23(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, Zero, Zero, h, ba) → new_glueVBal3GlueVBal26(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_r(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz147530, zzz147531, zzz147532, zzz147533, zzz147534), h, ba)
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), bb, bc) → zzz13792
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_glueVBal3Size_l(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714, zzz147530, zzz147531, zzz147532, zzz147533, zzz147534, h, ba) → new_sizeFM(Branch(zzz14710, zzz14711, zzz14712, zzz14713, zzz14714), h, ba)

The set Q consists of the following terms:

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



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

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

new_splitGT(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), h) → new_splitGT(zzz19934, h)
new_splitGT(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), h) → new_splitGT(zzz19934, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, h) → new_addToFM_C(zzz444, zzz41, h)
new_addToFM_C(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, h) → new_addToFM_C(zzz444, zzz41, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Zero, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch214(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch213(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Zero, bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Zero, bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), 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
                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), 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
                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), 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
                                    ↳ 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(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), 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
                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                                                                            ↳ 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(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Succ(zzz442000)), Succ(zzz442000))), Succ(Succ(zzz442000))), Succ(Succ(zzz442000))), 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
                                                                                            ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Succ(zzz442000)), Succ(zzz442000))), Succ(Succ(zzz442000))), Succ(Succ(zzz442000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primMulNat0(zzz550), Succ(zzz550)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Succ(zzz442000)), Succ(zzz442000))), Succ(Succ(zzz442000))), Succ(Succ(zzz442000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), 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
                                    ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Succ(zzz442000)), Succ(zzz442000))), Succ(Succ(zzz442000))), Succ(Succ(zzz442000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch29(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch14(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Succ(zzz442000)), Succ(zzz442000))), Succ(Succ(zzz442000))), Succ(Succ(zzz442000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch27(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch28(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch210(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ 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
                                                                                                                        ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), Succ(zzz55200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch22(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch21(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), 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
                                  ↳ 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
                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primMulNat0(zzz979), Succ(zzz979)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), 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
                                    ↳ 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
                                                                                                                        ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), 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
                                    ↳ 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
                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primMulNat0(zzz852), Succ(zzz852)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), 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
                                  ↳ 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
                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                                        ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), 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
                                  ↳ 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
                                                                                                                        ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), Succ(zzz979)), Succ(zzz979)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), 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
                                    ↳ 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
                                                                                                                        ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch17(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), Succ(zzz852)), Succ(zzz852)), bf) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), 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
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ 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(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979))), Succ(zzz979)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), 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
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852))), Succ(zzz852)), bf) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), 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
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), Succ(zzz550)), Succ(zzz550)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), 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
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                                              ↳ QDP
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                                                                  ↳ QDP
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                                                                      ↳ QDP
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                                                                                  ↳ QDP
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                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ QDP
                                                                                                    ↳ Rewriting
                                                                                                      ↳ QDP
                                                                                                        ↳ Rewriting
                                                                                                          ↳ QDP
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                                                                                                                ↳ Rewriting
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ DependencyGraphProof
                                                                                                                          ↳ QDP
                                                                                                                            ↳ Rewriting
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
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                                                                                                                                              ↳ QDP
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                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550))), Succ(zzz550)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), ba) → new_mkVBalBranch(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, ba)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
Used ordering: Polynomial interpretation [25]:

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

The following usable rules [17] were oriented: none



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch12(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, bc) → new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz550), zzz550)), zzz550)), zzz550))), bc)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), ba) → new_mkVBalBranch3MkVBalBranch11(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch212(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch29(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, bf) → new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz852), zzz852)), zzz852)), zzz852))), bf)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x3 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch1(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch10(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch11(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch12(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch13(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch14(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch15(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch16(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch2(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch20(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch212(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x3 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch23(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch24(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch25(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x3 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch26(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x3 + x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch29(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x3 + x6 + x7 + x8 + x9   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1)) = 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), bb) → new_mkVBalBranch(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), bb)
new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch13(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch29(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch1(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), h) → new_mkVBalBranch(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch23(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, ba)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch2(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), h) → new_mkVBalBranch3MkVBalBranch20(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, be) → new_mkVBalBranch3MkVBalBranch212(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, be)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, ba) → new_mkVBalBranch3MkVBalBranch10(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz979), zzz979)), zzz979)), zzz979))), ba)
new_mkVBalBranch3MkVBalBranch14(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), bf) → new_mkVBalBranch3MkVBalBranch16(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), bf)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), bd) → new_mkVBalBranch(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), bd)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch15(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), bc) → new_mkVBalBranch3MkVBalBranch16(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), bc)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch211(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs 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
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ UsableRulesProof
                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                  ↳ QReductionProof
                                                                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                              ↳ UsableRulesProof
                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                  ↳ QReductionProof
                                                                                                                                                                                                                                                                    ↳ 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_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), ba) → new_mkVBalBranch3MkVBalBranch20(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, ba)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                            ↳ 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_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz55200), zzz55200)), zzz55200))), h)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), bc) → new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, bc)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), be) → new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, be)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), h) → new_mkVBalBranch(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)
new_mkVBalBranch3MkVBalBranch26(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), be) → new_mkVBalBranch(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, be)
new_mkVBalBranch3MkVBalBranch25(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), bc) → new_mkVBalBranch(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, bc)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch26(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), h)
new_mkVBalBranch3MkVBalBranch24(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), h) → new_mkVBalBranch3MkVBalBranch25(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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
                                                                                            ↳ UsableRulesProof
                                                                                              ↳ QDP
                                                                                                ↳ QReductionProof
                                                                                                  ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, bd)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), bd) → new_mkVBalBranch3MkVBalBranch16(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, 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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, bb)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                                        ↳ 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
                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPOrderProof
                                                                                                                                                                                                                                                  ↳ 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_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), bb) → new_mkVBalBranch3MkVBalBranch11(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, 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
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT20(zzz79, zzz80, zzz81, zzz82, ba) → new_splitGT0(zzz81, ba)
new_splitGT0(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT20(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT21(zzz79, zzz80, zzz81, zzz82, ba) → new_splitGT0(zzz81, ba)
new_splitGT2(zzz917, zzz918, zzz919, Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT2(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT2(zzz917, zzz918, zzz919, Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT20(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT0(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT2(zzz9201, zzz9202, zzz9203, zzz9204, 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
                                  ↳ 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(zzz79, zzz80, zzz81, zzz82, ba) → new_splitGT0(zzz81, ba)
new_splitGT0(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT20(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT2(zzz917, zzz918, zzz919, Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT2(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT2(zzz917, zzz918, zzz919, Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT20(zzz9201, zzz9202, zzz9203, zzz9204, h)
new_splitGT0(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), h) → new_splitGT2(zzz9201, zzz9202, zzz9203, zzz9204, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C0(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, h) → new_addToFM_C0(zzz443, zzz41, h)
new_addToFM_C0(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, h) → new_addToFM_C0(zzz444, zzz41, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch231(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Zero, bd)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Zero, bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch3MkVBalBranch114(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch232(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch113(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch112(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch235(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch122(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch234(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch111(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch123(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), 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
                                  ↳ 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

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), 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
                                  ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, 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
                                  ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), 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
                                  ↳ 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

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), 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
                                  ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ca) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)



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

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch219(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch218(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch220(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, h)
new_mkVBalBranch3MkVBalBranch221(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 11 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), Succ(zzz54200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch228(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch227(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, h)
new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch226(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch118(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Succ(zzz442000)), Succ(Succ(zzz442000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ QDP
                                                                                                            ↳ Rewriting
                                                                                                              ↳ QDP
                                                                                                                ↳ DependencyGraphProof
                                                                                                                  ↳ QDP
                                                                                                                    ↳ Rewriting
                                                                                                                      ↳ QDP
                                                                                                                        ↳ Rewriting
                                                                                                                          ↳ QDP
                                                                                                                            ↳ DependencyGraphProof
                                                                                                                              ↳ QDP
                                                                                                                                ↳ Rewriting
                                                                                                                                  ↳ QDP
                                                                                                                                    ↳ Rewriting
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primMulNat0(zzz511), Succ(zzz511)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primMulNat0(zzz1147), Succ(zzz1147)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primMulNat0(zzz476), Succ(zzz476)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primMulNat0(zzz488), Succ(zzz488)), ca) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(Zero), Succ(Zero)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Succ(Zero)), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Succ(Zero)), Succ(Zero)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), Succ(zzz1147)), Succ(zzz1147)), bd) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), Succ(zzz476)), Succ(zzz476)), bb) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ UsableRulesProof
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ QReductionProof
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), Succ(zzz511)), Succ(zzz511)), bg) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), Succ(zzz488)), Succ(zzz488)), ca) at position [10,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), Succ(zzz44200)), Succ(zzz44200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero))), Succ(Zero)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511))), Succ(zzz511)), bg) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147))), Succ(zzz1147)), bd) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476))), Succ(zzz476)), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488))), Succ(zzz488)), ca) at position [10] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)



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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200))), Succ(zzz44200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch124(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)), Zero))), h) at position [10,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero)), Zero)))), h) at position [10,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(new_primPlusNat1(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero))))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(new_primPlusNat1(new_primPlusNat3(Zero), Zero))))), h) at position [10,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Zero)))))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(new_primPlusNat3(Zero)))))), h) at position [10,0,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), h) → new_mkVBalBranch3MkVBalBranch115(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), 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_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), bg) → new_mkVBalBranch3MkVBalBranch120(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), bg)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), 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 + x3 + x4 + x5   
POL(Neg(x1)) = 1   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
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 + x6   
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)) = x9   
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)) = 1 + x3 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch119(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x9   
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)) = x9   
POL(new_mkVBalBranch3MkVBalBranch18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10 + x3 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch217(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x3 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x3 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch222(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch223(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch224(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch225(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x3 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch227(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch229(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch230(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x3 + x6 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch233(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x9   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), be) → new_mkVBalBranch0(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), be)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch230(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch117(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, bg) → new_mkVBalBranch3MkVBalBranch118(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz511), zzz511)), zzz511)), zzz511))), bg)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch229(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd) → new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1147), zzz1147)), zzz1147)), zzz1147))), bd)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch119(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), bd) → new_mkVBalBranch3MkVBalBranch120(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), 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_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs 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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch3MkVBalBranch227(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, bf) → new_mkVBalBranch0(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, bf)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch227(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch225(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), h) → new_mkVBalBranch3MkVBalBranch224(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), bg) → new_mkVBalBranch0(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, bg)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), bd) → new_mkVBalBranch3MkVBalBranch224(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, bd)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch223(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), bg) → new_mkVBalBranch3MkVBalBranch225(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, bg)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
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_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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_mkVBalBranch3MkVBalBranch218(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch18(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(Succ(Succ(Succ(Zero))))), h)
new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch219(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), h) → new_mkVBalBranch0(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, bh) → new_mkVBalBranch3MkVBalBranch233(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch222(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
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)) = 1 + x1 + 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_mkVBalBranch3MkVBalBranch110(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10 + x3   
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)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch121(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x9   
POL(new_mkVBalBranch3MkVBalBranch18(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x9   
POL(new_mkVBalBranch3MkVBalBranch19(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x3 + x6   
POL(new_mkVBalBranch3MkVBalBranch217(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x3 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x3   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x3 + x9   
POL(new_mkVBalBranch3MkVBalBranch222(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x10 + x3   
POL(new_mkVBalBranch3MkVBalBranch233(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x3 + x9   
POL(new_primPlusNat1(x1, x2)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1)) = 0   

The following usable rules [17] were oriented: none



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch233(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ca) → new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz488), zzz488)), zzz488)), zzz488))), ca)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), bc) → new_mkVBalBranch0(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), bc)
new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)
new_mkVBalBranch3MkVBalBranch121(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ca) → new_mkVBalBranch3MkVBalBranch115(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ca)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), h) → new_mkVBalBranch3MkVBalBranch19(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch222(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, bb) → new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz476), zzz476)), zzz476)), zzz476))), bb)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ba) → new_mkVBalBranch3MkVBalBranch218(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ba)
new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch116(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz44200), zzz44200)), zzz44200)), zzz44200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch219(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb) → new_mkVBalBranch3MkVBalBranch233(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, cb)
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)
new_mkVBalBranch3MkVBalBranch110(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), bb) → new_mkVBalBranch3MkVBalBranch115(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), bb)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 3 SCCs with 10 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                                                                                                                                                                                                                                                                                                                ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                                                                                                                                                                                                                                                                                                                ↳ 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(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                                                                                                                                                                                                                                                                                                                ↳ 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(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), h) → new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, 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
                                                                                ↳ Rewriting
                                                                                  ↳ QDP
                                                                                    ↳ Rewriting
                                                                                      ↳ QDP
                                                                                        ↳ Rewriting
                                                                                          ↳ QDP
                                                                                            ↳ Rewriting
                                                                                              ↳ QDP
                                                                                                ↳ Rewriting
                                                                                                  ↳ QDP
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                                                                                                                                                                                                                                                                                                                ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch0(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), h) → new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz54200), zzz54200)), zzz54200))), h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ba) → new_mkVBalBranch0(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ba)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch216(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, h)
new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ba) → new_mkVBalBranch3MkVBalBranch216(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ba)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), bh) → new_mkVBalBranch0(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, bh)
new_mkVBalBranch3MkVBalBranch215(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), h) → new_mkVBalBranch3MkVBalBranch217(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, h)
new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), bh) → new_mkVBalBranch3MkVBalBranch217(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, bh)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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



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

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

new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, bc)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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
                                                                                                                                                                                                                                                                                                                              ↳ 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_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), bc) → new_mkVBalBranch3MkVBalBranch115(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, 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
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                    ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, be)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                                                    ↳ UsableRulesProof
                                                                                                      ↳ QDP
                                                                                                        ↳ QReductionProof
                                                                                                          ↳ 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
                                                                                                                                                                            ↳ 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
                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ 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_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), be) → new_mkVBalBranch3MkVBalBranch120(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitGT1(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), h) → new_splitGT23(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitGT23(zzz902, zzz903, zzz904, zzz905, ba) → new_splitGT1(zzz904, ba)
new_splitGT1(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), h) → new_splitGT22(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitGT22(zzz886, zzz887, Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), zzz889, h) → new_splitGT22(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitGT22(zzz886, zzz887, Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), zzz889, h) → new_splitGT23(zzz8881, zzz8882, zzz8883, zzz8884, 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT2(zzz886, zzz887, Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), zzz889, h) → new_splitLT2(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitLT20(zzz902, zzz903, zzz904, zzz905, ba) → new_splitLT(zzz904, ba)
new_splitLT(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), h) → new_splitLT2(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitLT2(zzz886, zzz887, Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), zzz889, h) → new_splitLT20(zzz8881, zzz8882, zzz8883, zzz8884, h)
new_splitLT(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), h) → new_splitLT20(zzz8881, zzz8882, zzz8883, zzz8884, 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
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_addToFM_C1(Branch(EQ, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, h) → new_addToFM_C1(zzz3193, zzz41, h)
new_addToFM_C1(Branch(GT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, h) → new_addToFM_C1(zzz3193, zzz41, 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Zero, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), 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
                                  ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), 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
                                  ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), 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
                                  ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), 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
                                  ↳ 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_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), 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
                                  ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), 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
                                  ↳ 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_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primMulNat1(x0)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), Succ(zzz43200)), Succ(zzz43200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primMulNat0(zzz1022), Succ(zzz1022)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primMulNat0(zzz1008), Succ(zzz1008)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primMulNat0(x0)
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), Succ(zzz1008)), Succ(zzz1008)), ba) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch244(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200))), Succ(zzz43200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch239(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch240(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), Succ(zzz1022)), Succ(zzz1022)), bc) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008))), Succ(zzz1008)), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022))), Succ(zzz1022)), bc) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), Succ(zzz319200)), Succ(zzz319200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200))), Succ(zzz319200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, h) → new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch132(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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 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
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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


The following pairs can be oriented strictly and are deleted.


new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc) → new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1022), zzz1022)), zzz1022)), zzz1022))), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba) → new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz1008), zzz1008)), zzz1008)), zzz1008))), ba)
new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x4 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch1(x1, x2, x3, x4)) = x2   
POL(new_mkVBalBranch3MkVBalBranch125(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x7   
POL(new_mkVBalBranch3MkVBalBranch126(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch127(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch128(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch129(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x6 + x7 + x8 + x9   
POL(new_mkVBalBranch3MkVBalBranch130(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x10   
POL(new_mkVBalBranch3MkVBalBranch131(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch236(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch237(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch238(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = 1 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch241(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x6 + x9   
POL(new_mkVBalBranch3MkVBalBranch242(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch243(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch245(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x10 + x7 + x9   
POL(new_primPlusNat1(x1, x2)) = 1 + x1   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1)) = 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), bb) → new_mkVBalBranch1(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch128(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch3MkVBalBranch130(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), bc) → new_mkVBalBranch3MkVBalBranch131(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), bc)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch245(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, bc)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch126(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), ba) → new_mkVBalBranch3MkVBalBranch127(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), bd) → new_mkVBalBranch1(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), bd)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch238(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch125(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz319200), zzz319200)), zzz319200)), zzz319200))), h)
new_mkVBalBranch3MkVBalBranch129(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), h) → new_mkVBalBranch1(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch241(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, ba)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 6 SCCs with 10 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                              ↳ UsableRulesProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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
                                                                        ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                              ↳ 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_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                              ↳ QDPSizeChangeProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), bc) → new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, bc)
new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch243(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), bc) → new_mkVBalBranch1(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, bc)
new_mkVBalBranch3MkVBalBranch242(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), h) → new_mkVBalBranch3MkVBalBranch243(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, h)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



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

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), h) → new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, 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
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                              ↳ QDPSizeChangeProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch1(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), h) → new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(Succ(new_primPlusNat2(Succ(new_primPlusNat2(Succ(new_primPlusNat1(new_primPlusNat3(zzz43200), zzz43200)), zzz43200)), zzz43200))), h)
new_mkVBalBranch3MkVBalBranch236(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), h) → new_mkVBalBranch3MkVBalBranch237(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, h)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), ba) → new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, ba)
new_mkVBalBranch3MkVBalBranch237(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), ba) → new_mkVBalBranch1(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, ba)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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



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

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

new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, bb)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



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

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

new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), bb) → new_mkVBalBranch3MkVBalBranch127(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ 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
                                                                                                                                            ↳ Rewriting
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ Rewriting
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                              ↳ 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
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ UsableRulesProof
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP

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

new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)

The TRS R consists of the following rules:

new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat3(Zero) → Zero
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Zero, Zero) → Zero
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)

The set Q consists of the following terms:

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

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

new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, bd)

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

new_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(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_primPlusNat2(Zero, Succ(x0))
new_primPlusNat3(Zero)
new_primPlusNat2(Succ(x0), Zero)
new_primPlusNat3(Succ(x0))
new_primPlusNat1(x0, Zero)
new_primPlusNat2(Succ(x0), Succ(x1))
new_primPlusNat2(Zero, Zero)
new_primPlusNat1(x0, Succ(x1))



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

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

new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), bd) → new_mkVBalBranch3MkVBalBranch131(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ QDPSizeChangeProof
                                  ↳ QDP
                                  ↳ QDP

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

new_splitLT0(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), h) → new_splitLT0(zzz19934, h)
new_splitLT0(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), h) → new_splitLT0(zzz19934, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                  ↳ QDP

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

new_splitLT22(zzz79, zzz80, Branch(LT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT1(zzz814, h)
new_splitLT22(zzz79, zzz80, Branch(GT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT21(zzz811, zzz812, zzz813, zzz814, h)
new_splitLT21(zzz79, zzz80, Branch(GT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT21(zzz811, zzz812, zzz813, zzz814, h)
new_splitLT1(Branch(GT, zzz811, zzz812, zzz813, zzz814), h) → new_splitLT21(zzz811, zzz812, zzz813, zzz814, h)
new_splitLT21(zzz79, zzz80, Branch(LT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT1(zzz814, h)
new_splitLT1(Branch(LT, zzz811, zzz812, zzz813, zzz814), h) → new_splitLT1(zzz814, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof
                                      ↳ QDP
                                        ↳ QDPSizeChangeProof
                                  ↳ QDP

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

new_splitLT21(zzz79, zzz80, Branch(GT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT21(zzz811, zzz812, zzz813, zzz814, h)
new_splitLT1(Branch(GT, zzz811, zzz812, zzz813, zzz814), h) → new_splitLT21(zzz811, zzz812, zzz813, zzz814, h)
new_splitLT21(zzz79, zzz80, Branch(LT, zzz811, zzz812, zzz813, zzz814), zzz82, h) → new_splitLT1(zzz814, h)
new_splitLT1(Branch(LT, zzz811, zzz812, zzz813, zzz814), h) → new_splitLT1(zzz814, 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
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                    ↳ DependencyGraphProof

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

new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, GT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz914, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C15(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, LT, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz930, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz43331, zzz43332, zzz43333, zzz43334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444)), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C11(zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444), zzz3, zzz51, zzz52, zzz53, zzz54, zzz440, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT4(zzz41, zzz42, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, GT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz898, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT6(bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, EmptyFM, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT8(zzz431, zzz432, zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, EmptyFM))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT11(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT10(zzz41, zzz42, zzz43, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT23(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(EQ, zzz41, zzz42, zzz43, zzz44), zzz3, zzz51, zzz52, zzz53, zzz54, zzz41, zzz42, zzz43, zzz44, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT8(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT5(zzz41, zzz42, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT5(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, EmptyFM, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT8(zzz431, zzz432, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz4331, zzz4332, zzz4333, zzz4334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz4441, zzz4442, zzz4443, zzz4444, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C10(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz431, zzz432, zzz433, zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz44441, zzz44442, zzz44443, zzz44444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C16(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C13(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, EmptyFM)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT10(zzz41, zzz42, zzz43, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), zzz3, zzz51, zzz52, zzz53, zzz54, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT4(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz44441, zzz44442, zzz44443, zzz44444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, EmptyFM)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, EmptyFM))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT11(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT7(zzz431, zzz432, zzz433, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C13(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C14(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444441, zzz444442, zzz444443, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C15(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT6(bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT24(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT8(zzz41, zzz42, zzz44, bb), zzz53, h, ba, bb)

The TRS R consists of the following rules:

new_splitLT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitLT26(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, zzz542, zzz543, zzz544), EmptyFM, bb) → new_addToFM1(Branch(zzz540, zzz541, zzz542, zzz543, zzz544), zzz41, bb)
new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT23(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT17(zzz81, db)
new_splitGT18(Branch(EQ, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT210(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), fa) → new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, fa)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20140), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20140, Zero, dh, ea)
new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz1836, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch2(zzz41, EmptyFM, zzz319, bb) → new_addToFM2(zzz319, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20130), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT19(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20410), zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20410, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_addToFM_C2(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(GT, zzz441, new_addToFM_C2(zzz443, zzz41, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20120), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_addToFM2(zzz319, zzz41, bb) → new_addToFM_C3(zzz319, zzz41, bb)
new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch147(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, EmptyFM, dh, ea) → error([])
new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Zero)), zzz1475340, zzz1475341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz147530, zzz147531, zzz1836, zzz1475343, dh, ea), zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1862, Branch(zzz1857, zzz1858, Neg(Succ(zzz1859)), zzz1860, zzz1861), Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), eb)
new_splitGT12(EmptyFM, df) → new_splitGT42(df)
new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitLT17(Branch(LT, zzz917, zzz918, zzz919, zzz920), ce)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_addToFM_C3(Branch(EQ, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(EQ, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19720), dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz19720, Zero, dh, ea)
new_mkBalBranch(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, new_primPlusInt2(new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz1990000, zzz201500, dh, ea)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1369, Branch(zzz1364, zzz1365, Neg(Succ(zzz1366)), zzz1367, zzz1368), Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef) → new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), ef)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), ff) → new_mkBalBranch(zzz1692, zzz1693, zzz1695, new_mkVBalBranch3(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ff), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Zero, zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_addToFM_C2(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C2(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb) → new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), fb)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch256(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), bb)
new_splitLT18(bb) → new_splitLT40(bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc) → new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), gc)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, EmptyFM, zzz1475344, dh, ea) → error([])
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Succ(zzz19650), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz19650, dh, ea)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_splitLT6(bb) → new_splitLT41(bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), EmptyFM, bb) → new_addToFM2(Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz41, bb)
new_primMulNat2(Succ(zzz199100)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz199100)), Succ(zzz199100))
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_splitGT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_splitGT10(zzz441, zzz442, zzz443, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), gd)
new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), fa) → new_mkBalBranch(zzz1857, zzz1858, zzz1860, new_mkVBalBranch4(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), fa), ty_Ordering, fa)
new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), fb)
new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz1961000, zzz196500, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2036, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), fb) → new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, fb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_primPlusInt(zzz13430, Pos(zzz14600)) → Pos(new_primPlusNat2(zzz13430, zzz14600))
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, bb)
new_splitGT16(bb) → new_splitGT40(bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), ef) → new_mkBalBranch(zzz509, zzz510, new_mkVBalBranch4(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, ef), zzz513, ty_Ordering, ef)
new_splitLT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch2(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_splitGT40(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, zzz552, zzz553, zzz554), EmptyFM, bb) → new_addToFM(Branch(zzz550, zzz551, zzz552, zzz553, zzz554), zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd) → new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), gd)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), gh) → new_mkBalBranch(zzz1159, zzz1160, new_mkVBalBranch3(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, gh), zzz1163, ty_Ordering, gh)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), eg)
new_splitGT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT29(zzz79, zzz80, zzz81, zzz82, db)
new_primPlusInt1(zzz13430, Pos(zzz14650)) → new_primMinusNat0(zzz14650, zzz13430)
new_splitLT17(Branch(GT, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT24(zzz811, zzz812, zzz813, zzz814, db)
new_mkVBalBranch3(zzz41, EmptyFM, zzz44, bb) → new_addToFM(zzz44, zzz41, bb)
new_intersectFM_C2Lts0(zzz1993, df) → new_splitLT12(zzz1993, df)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ge) → new_mkVBalBranch3MkVBalBranch284(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb)
new_splitGT8(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT6(bb), zzz44, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), ha) → new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, ha)
new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT18(zzz920, ce)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Zero, fb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), ed) → new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, ed)
new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitGT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT18(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT26(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT16(zzz904, ca)
new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, EmptyFM, zzz147534, dh, ea) → error([])
new_addToFM_C4(EmptyFM, zzz41, bb) → Branch(GT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), ec) → new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, ec)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, Branch(zzz183640, zzz183641, zzz183642, zzz183643, zzz183644), zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz183640, zzz183641, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz18360, zzz18361, zzz18363, zzz183643, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz147530, zzz147531, zzz183644, zzz147534, dh, ea), dh, ea)
new_primPlusInt2(Neg(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt1(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT4(zzz41, zzz42, zzz44, bb) → new_splitLT15(bb)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1969, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), ed) → new_mkBalBranch(zzz1756, zzz1757, zzz1759, new_mkVBalBranch4(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ed), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, eh)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch290(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_splitLT40(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, EmptyFM, zzz147534, dh, ea) → error([])
new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT14(zzz441, zzz442, zzz443, zzz444, bb), bb)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19670), dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz19670, dh, ea)
new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), bb)
new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea)
new_splitLT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch4(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, bb)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2027000, zzz203500, dh, ea)
new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitGT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT27(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_addToFM0(zzz441, zzz41, bb) → zzz41
new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2007, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, bb)
new_splitGT42(bb) → new_emptyFM(bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), gc) → new_mkBalBranch(zzz1006, zzz1007, new_mkVBalBranch2(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, gc), zzz1010, ty_Ordering, gc)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Succ(zzz20030), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz20030, dh, ea)
new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT9(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Zero)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1697, Branch(zzz1692, zzz1693, Neg(Succ(zzz1694)), zzz1695, zzz1696), Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), ef)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, bb)
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_splitGT41(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz1988000, zzz200300, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), bb)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20100), dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz20100, Zero, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20080), zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz20080, zzz198800, dh, ea)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT18(EmptyFM, ce) → new_splitGT41(ce)
new_addToFM_C4(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(GT, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Succ(zzz20150), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, zzz20150, dh, ea)
new_primMinusNat0(Succ(zzz94600), Zero) → Pos(Succ(zzz94600))
new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_sizeFM(EmptyFM, ga, gb) → Pos(Zero)
new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Succ(Zero), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20050), dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz20050, dh, ea)
new_splitGT19(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch284(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, bb)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch251(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT29(zzz886, zzz887, zzz888, zzz889, be)
new_splitLT10(zzz41, zzz42, zzz43, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT18(bb), bb)
new_primPlusInt0(Pos(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_splitGT19(EmptyFM, be) → new_splitGT40(be)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ee)
new_addToFM_C2(EmptyFM, zzz41, bb) → Branch(EQ, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_primPlusInt0(Neg(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt1(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT29(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT24(zzz79, zzz80, zzz81, zzz82, db)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2041, dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2041, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb) → new_splitGT14(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb)
new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Succ(zzz20350), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz20350, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch284(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), eb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, ha) → new_mkVBalBranch3MkVBalBranch289(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_splitLT8(zzz41, zzz42, zzz44, bb) → new_splitLT6(bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), gd) → new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, gd)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19680), dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, bb)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20430), dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20430, Zero, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb)
new_primMulNat(Zero) → Zero
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh) → new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), eh)
new_primPlusInt2(Pos(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20420), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), fc) → new_mkBalBranch(zzz1364, zzz1365, zzz1367, new_mkVBalBranch2(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), fc), ty_Ordering, fc)
new_addToFM_C4(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2008, dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, zzz2008, zzz198800, dh, ea)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), ec)
new_splitGT4(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch4(zzz41, new_splitGT16(bb), zzz44, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), gg) → new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, gg)
new_mkVBalBranch3MkVBalBranch256(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, gf) → new_mkBalBranch(zzz497, zzz498, new_mkVBalBranch4(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, gf), zzz501, ty_Ordering, gf)
new_splitGT24(zzz79, zzz80, zzz81, zzz82, db) → new_mkVBalBranch3(zzz79, new_splitGT18(zzz81, db), zzz82, db)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_splitLT16(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT29(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Zero, ec)
new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_addToFM_C3(Branch(LT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → Branch(LT, new_addToFM0(zzz3191, zzz41, bb), zzz3192, zzz3193, zzz3194)
new_splitGT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_addToFM1(zzz44, zzz41, bb) → new_addToFM_C2(zzz44, zzz41, bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), gc) → new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, gc)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ge) → new_mkVBalBranch3MkVBalBranch285(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), fd) → new_mkBalBranch(zzz1350, zzz1351, zzz1353, new_mkVBalBranch2(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), fd), ty_Ordering, fd)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Succ(zzz18660000)))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ee)
new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), eg)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT9(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1970, dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, zzz1970, zzz196100, dh, ea)
new_mkVBalBranch3MkVBalBranch290(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb) → new_mkVBalBranch3MkVBalBranch289(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_splitLT16(EmptyFM, be) → new_splitLT42(be)
new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca) → new_mkVBalBranch3(zzz902, new_splitGT19(zzz904, ca), zzz905, ca)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), eb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), fc) → new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, fc)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch256(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, Branch(zzz14753430, zzz14753431, zzz14753432, zzz14753433, zzz14753434), zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz14753430, zzz14753431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz147530, zzz147531, zzz1836, zzz14753433, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz1475340, zzz1475341, zzz14753434, zzz1475344, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1761, Branch(zzz1756, zzz1757, Pos(Succ(zzz1758)), zzz1759, zzz1760), Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), fb) → new_mkBalBranch(zzz548, zzz549, new_mkVBalBranch3(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, fb), zzz552, ty_Ordering, fb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitLT16(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_splitGT15(zzz441, zzz442, zzz443, zzz444, bb)
new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20060), dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1966, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), gg) → new_mkBalBranch(zzz1843, zzz1844, zzz1846, new_mkVBalBranch3(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), gg), ty_Ordering, gg)
new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitGT211(zzz886, zzz887, zzz888, zzz889, be)
new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_splitLT17(Branch(LT, zzz811, zzz812, zzz813, zzz814), db) → new_mkVBalBranch2(zzz811, zzz813, new_splitLT17(zzz814, db), db)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz18360, zzz18361, zzz18363, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz147530, zzz147531, zzz18364, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Zero))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz186600)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, gh) → new_mkVBalBranch3MkVBalBranch251(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT10(zzz441, zzz442, zzz443, bb), bb)
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), ga, gb) → zzz13792
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), gc)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch289(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitGT211(zzz886, zzz887, zzz888, zzz889, be) → new_mkVBalBranch4(zzz886, new_splitGT19(zzz888, be), zzz889, be)
new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_addToFM_C4(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(EQ, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), bb)
new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2004, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT15(bb) → new_splitLT42(bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_primPlusInt(zzz13430, Neg(zzz14600)) → new_primMinusNat0(zzz13430, zzz14600)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20380), dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz20380, dh, ea)
new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, zzz1959, dh, ea) → new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz1959, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20110), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz20110, dh, ea)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ge) → new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ge)
new_splitLT17(Branch(EQ, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT27(zzz811, zzz812, zzz813, zzz814, db)
new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitLT42(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20090), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_emptyFM(h) → EmptyFM
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), ff) → new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, ff)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitGT6(bb) → new_splitGT41(bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT17(EmptyFM, db) → new_splitLT41(db)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, bb)
new_splitGT18(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT29(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), ef) → new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, ef)
new_primPlusNat3(Zero) → Zero
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), ec) → new_mkBalBranch(zzz1020, zzz1021, new_mkVBalBranch2(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, ec), zzz1024, ty_Ordering, ec)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), gd) → new_mkBalBranch(zzz977, zzz978, new_mkVBalBranch3(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, gd), zzz981, ty_Ordering, gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), gd)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_primMinusNat0(Zero, Succ(zzz642000)) → Neg(Succ(zzz642000))
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Zero, eh)
new_splitGT5(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT16(bb), zzz44, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_primPlusInt1(zzz13430, Neg(zzz14650)) → Neg(new_primPlusNat2(zzz13430, zzz14650))
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), fd) → new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, fd)
new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_primPlusNat2(Zero, Zero) → Zero
new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_splitLT24(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT23(zzz79, zzz80, zzz81, zzz82, db)
new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1355, Branch(zzz1350, zzz1351, Pos(Succ(zzz1352)), zzz1353, zzz1354), Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), ty_Ordering, fd)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20390), dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, Branch(zzz18360, zzz18361, zzz18362, zzz18363, zzz18364), zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_sizeFM(zzz18364, dh, ea), new_sizeFM(zzz18363, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_splitLT5(zzz41, zzz42, zzz44, bb) → new_splitLT15(bb)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19710), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkBranch(zzz2030, zzz2031, zzz2032, zzz2033, zzz2034, fg, fh) → Branch(zzz2031, zzz2032, new_primPlusInt0(new_primPlusInt(Succ(Zero), new_sizeFM(zzz2033, fg, fh)), zzz2034, zzz2031, zzz2033, fg, fh), zzz2033, zzz2034)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ge) → new_mkBalBranch(zzz1114, zzz1115, new_mkVBalBranch4(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ge), zzz1118, ty_Ordering, ge)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec) → new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), ec)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), eh)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_addToFM_C3(EmptyFM, zzz41, bb) → Branch(LT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), gh) → new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, gh)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19700), zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz19700, zzz196100, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20160), zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20160, zzz199000, dh, ea)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch251(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg)
new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce)
new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_splitGT17(bb) → new_splitGT42(bb)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Zero, ef)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, bb)
new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1848, Branch(zzz1843, zzz1844, Pos(Succ(zzz1845)), zzz1846, zzz1847), Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_splitLT41(bb) → new_emptyFM(bb)
new_splitGT19(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT211(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT10(zzz41, zzz42, zzz43, bb) → new_splitGT17(bb)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, gh) → new_mkVBalBranch3MkVBalBranch252(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_splitLT12(EmptyFM, df) → new_splitLT40(df)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_splitLT29(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT16(zzz888, be)
new_intersectFM_C2Gts0(zzz1993, df) → new_splitGT12(zzz1993, df)
new_mkVBalBranch4(zzz41, EmptyFM, zzz44, bb) → new_addToFM1(zzz44, zzz41, bb)
new_addToFM_C3(Branch(GT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(GT, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), zzz199000, dh, ea)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), ha) → new_mkBalBranch(zzz952, zzz953, new_mkVBalBranch4(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, ha), zzz956, ty_Ordering, ha)
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, ha) → new_mkVBalBranch3MkVBalBranch290(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2040, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), bb)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, Branch(zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344), dh, ea) → new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_sizeFM(zzz1475343, dh, ea), new_sizeFM(zzz1475344, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_splitLT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT24(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_splitLT16(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_addToFM(zzz44, zzz41, bb) → new_addToFM_C4(zzz44, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_addToFM_C2(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(EQ, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Zero, eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Zero, eg)
new_primMinusNat0(Succ(zzz94600), Succ(zzz642000)) → new_primMinusNat0(zzz94600, zzz642000)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch281(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT18(x0)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT14(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT19(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT41(x0)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primMulNat0(x0)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch269(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_primPlusNat2(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Zero, x5, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_splitGT8(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_splitGT16(x0)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch30(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT16(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch292(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Zero, Zero)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_addToFM1(x0, x1, x2)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5)
new_primPlusNat1(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primPlusInt(x0, Neg(x1))
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(EmptyFM, x0, x1)
new_splitGT211(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Gts0(x0, x1)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT17(EmptyFM, x0)
new_splitLT6(x0)
new_splitLT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_splitGT18(Branch(LT, x0, x1, x2, x3), x4)
new_splitGT19(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch284(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT4(x0, x1, x2, x3)
new_primMulNat(Zero)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_primPlusInt(x0, Pos(x1))
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_primPlusInt0(Pos(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusInt1(x0, Pos(x1))
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
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_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitLT23(x0, x1, x2, x3, x4)
new_splitGT15(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, x4, x5)
new_intersectFM_C2Lts3(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primMulNat1(x0)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_splitGT18(EmptyFM, x0)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_intersectFM_C2Gts3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT13(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitLT28(x0, x1, x2, x3, x4)
new_primPlusNat2(Succ(x0), Succ(x1))
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitLT16(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT17(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(x0)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT17(x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT14(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT16(EmptyFM, x0)
new_splitLT26(x0, x1, x2, x3, x4)
new_primPlusNat3(Succ(x0))
new_splitLT42(x0)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat2(Succ(x0))
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_intersectFM_C2Lts0(x0, x1)
new_addToFM2(x0, x1, x2)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT12(EmptyFM, x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitGT13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch273(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, Zero, x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_splitGT19(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch268(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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusNat3(Zero)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitLT16(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitGT42(x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitLT10(x0, x1, x2, x3)
new_splitGT18(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
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, Succ(x10), x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch261(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusNat1(x0, Zero)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_splitGT6(x0)
new_mkBalBranch6MkBalBranch30(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_emptyFM(x0)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch291(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(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_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_splitGT5(x0, x1, x2, x3)
new_primPlusInt0(Neg(x0), x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT17(Branch(GT, x0, x1, x2, x3), x4)
new_primPlusInt1(x0, Neg(x1))
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_splitLT17(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_addToFM(x0, x1, x2)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_splitGT24(x0, x1, x2, x3, x4)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT18(Branch(GT, x0, x1, x2, x3), x4)
new_splitGT7(x0, x1, x2, x3, x4)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch171(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, x10, x11)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_primMulNat(Succ(x0))
new_splitLT27(x0, x1, x2, x3, x4)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch267(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_sizeFM(EmptyFM, x0, x1)
new_splitGT19(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)

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

↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, GT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz914, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C15(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, LT, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz930, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz43331, zzz43332, zzz43333, zzz43334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444)), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C11(zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444), zzz3, zzz51, zzz52, zzz53, zzz54, zzz440, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, GT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz898, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT6(bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, EmptyFM))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT11(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT23(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT8(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(EQ, zzz41, zzz42, zzz43, zzz44), zzz3, zzz51, zzz52, zzz53, zzz54, zzz41, zzz42, zzz43, zzz44, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT5(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, EmptyFM, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT8(zzz431, zzz432, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz4331, zzz4332, zzz4333, zzz4334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz4441, zzz4442, zzz4443, zzz4444, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C10(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz431, zzz432, zzz433, zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz44441, zzz44442, zzz44443, zzz44444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C16(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C13(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT10(zzz41, zzz42, zzz43, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), zzz3, zzz51, zzz52, zzz53, zzz54, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT4(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz44441, zzz44442, zzz44443, zzz44444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, EmptyFM)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT7(zzz431, zzz432, zzz433, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C13(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C14(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444441, zzz444442, zzz444443, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C15(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT24(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)

The TRS R consists of the following rules:

new_splitLT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitLT26(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, zzz542, zzz543, zzz544), EmptyFM, bb) → new_addToFM1(Branch(zzz540, zzz541, zzz542, zzz543, zzz544), zzz41, bb)
new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT23(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT17(zzz81, db)
new_splitGT18(Branch(EQ, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT210(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), fa) → new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, fa)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20140), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20140, Zero, dh, ea)
new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz1836, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch2(zzz41, EmptyFM, zzz319, bb) → new_addToFM2(zzz319, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20130), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT19(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20410), zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20410, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_addToFM_C2(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(GT, zzz441, new_addToFM_C2(zzz443, zzz41, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20120), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_addToFM2(zzz319, zzz41, bb) → new_addToFM_C3(zzz319, zzz41, bb)
new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch147(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, EmptyFM, dh, ea) → error([])
new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Zero)), zzz1475340, zzz1475341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz147530, zzz147531, zzz1836, zzz1475343, dh, ea), zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1862, Branch(zzz1857, zzz1858, Neg(Succ(zzz1859)), zzz1860, zzz1861), Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), eb)
new_splitGT12(EmptyFM, df) → new_splitGT42(df)
new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitLT17(Branch(LT, zzz917, zzz918, zzz919, zzz920), ce)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_addToFM_C3(Branch(EQ, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(EQ, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19720), dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz19720, Zero, dh, ea)
new_mkBalBranch(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, new_primPlusInt2(new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz1990000, zzz201500, dh, ea)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1369, Branch(zzz1364, zzz1365, Neg(Succ(zzz1366)), zzz1367, zzz1368), Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef) → new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), ef)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), ff) → new_mkBalBranch(zzz1692, zzz1693, zzz1695, new_mkVBalBranch3(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ff), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Zero, zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_addToFM_C2(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C2(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb) → new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), fb)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch256(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), bb)
new_splitLT18(bb) → new_splitLT40(bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc) → new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), gc)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, EmptyFM, zzz1475344, dh, ea) → error([])
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Succ(zzz19650), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz19650, dh, ea)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_splitLT6(bb) → new_splitLT41(bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), EmptyFM, bb) → new_addToFM2(Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz41, bb)
new_primMulNat2(Succ(zzz199100)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz199100)), Succ(zzz199100))
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_splitGT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_splitGT10(zzz441, zzz442, zzz443, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), gd)
new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), fa) → new_mkBalBranch(zzz1857, zzz1858, zzz1860, new_mkVBalBranch4(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), fa), ty_Ordering, fa)
new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), fb)
new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz1961000, zzz196500, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2036, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), fb) → new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, fb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_primPlusInt(zzz13430, Pos(zzz14600)) → Pos(new_primPlusNat2(zzz13430, zzz14600))
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, bb)
new_splitGT16(bb) → new_splitGT40(bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), ef) → new_mkBalBranch(zzz509, zzz510, new_mkVBalBranch4(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, ef), zzz513, ty_Ordering, ef)
new_splitLT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch2(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_splitGT40(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, zzz552, zzz553, zzz554), EmptyFM, bb) → new_addToFM(Branch(zzz550, zzz551, zzz552, zzz553, zzz554), zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd) → new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), gd)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), gh) → new_mkBalBranch(zzz1159, zzz1160, new_mkVBalBranch3(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, gh), zzz1163, ty_Ordering, gh)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), eg)
new_splitGT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT29(zzz79, zzz80, zzz81, zzz82, db)
new_primPlusInt1(zzz13430, Pos(zzz14650)) → new_primMinusNat0(zzz14650, zzz13430)
new_splitLT17(Branch(GT, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT24(zzz811, zzz812, zzz813, zzz814, db)
new_mkVBalBranch3(zzz41, EmptyFM, zzz44, bb) → new_addToFM(zzz44, zzz41, bb)
new_intersectFM_C2Lts0(zzz1993, df) → new_splitLT12(zzz1993, df)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ge) → new_mkVBalBranch3MkVBalBranch284(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb)
new_splitGT8(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT6(bb), zzz44, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), ha) → new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, ha)
new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT18(zzz920, ce)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Zero, fb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), ed) → new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, ed)
new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitGT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT18(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT26(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT16(zzz904, ca)
new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, EmptyFM, zzz147534, dh, ea) → error([])
new_addToFM_C4(EmptyFM, zzz41, bb) → Branch(GT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), ec) → new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, ec)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, Branch(zzz183640, zzz183641, zzz183642, zzz183643, zzz183644), zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz183640, zzz183641, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz18360, zzz18361, zzz18363, zzz183643, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz147530, zzz147531, zzz183644, zzz147534, dh, ea), dh, ea)
new_primPlusInt2(Neg(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt1(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT4(zzz41, zzz42, zzz44, bb) → new_splitLT15(bb)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1969, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), ed) → new_mkBalBranch(zzz1756, zzz1757, zzz1759, new_mkVBalBranch4(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ed), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, eh)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch290(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_splitLT40(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, EmptyFM, zzz147534, dh, ea) → error([])
new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT14(zzz441, zzz442, zzz443, zzz444, bb), bb)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19670), dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz19670, dh, ea)
new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), bb)
new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea)
new_splitLT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch4(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, bb)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2027000, zzz203500, dh, ea)
new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitGT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT27(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_addToFM0(zzz441, zzz41, bb) → zzz41
new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2007, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, bb)
new_splitGT42(bb) → new_emptyFM(bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), gc) → new_mkBalBranch(zzz1006, zzz1007, new_mkVBalBranch2(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, gc), zzz1010, ty_Ordering, gc)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Succ(zzz20030), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz20030, dh, ea)
new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT9(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Zero)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1697, Branch(zzz1692, zzz1693, Neg(Succ(zzz1694)), zzz1695, zzz1696), Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), ef)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, bb)
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_splitGT41(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz1988000, zzz200300, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), bb)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20100), dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz20100, Zero, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20080), zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz20080, zzz198800, dh, ea)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT18(EmptyFM, ce) → new_splitGT41(ce)
new_addToFM_C4(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(GT, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Succ(zzz20150), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, zzz20150, dh, ea)
new_primMinusNat0(Succ(zzz94600), Zero) → Pos(Succ(zzz94600))
new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_sizeFM(EmptyFM, ga, gb) → Pos(Zero)
new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Succ(Zero), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20050), dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz20050, dh, ea)
new_splitGT19(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch284(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, bb)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch251(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT29(zzz886, zzz887, zzz888, zzz889, be)
new_splitLT10(zzz41, zzz42, zzz43, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT18(bb), bb)
new_primPlusInt0(Pos(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_splitGT19(EmptyFM, be) → new_splitGT40(be)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ee)
new_addToFM_C2(EmptyFM, zzz41, bb) → Branch(EQ, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_primPlusInt0(Neg(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt1(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT29(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT24(zzz79, zzz80, zzz81, zzz82, db)
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2041, dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2041, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb) → new_splitGT14(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb)
new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Succ(zzz20350), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz20350, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch284(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), eb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, ha) → new_mkVBalBranch3MkVBalBranch289(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_splitLT8(zzz41, zzz42, zzz44, bb) → new_splitLT6(bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), gd) → new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, gd)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19680), dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, bb)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20430), dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20430, Zero, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb)
new_primMulNat(Zero) → Zero
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh) → new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), eh)
new_primPlusInt2(Pos(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20420), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), fc) → new_mkBalBranch(zzz1364, zzz1365, zzz1367, new_mkVBalBranch2(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), fc), ty_Ordering, fc)
new_addToFM_C4(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2008, dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, zzz2008, zzz198800, dh, ea)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), ec)
new_splitGT4(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch4(zzz41, new_splitGT16(bb), zzz44, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), gg) → new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, gg)
new_mkVBalBranch3MkVBalBranch256(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, gf) → new_mkBalBranch(zzz497, zzz498, new_mkVBalBranch4(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, gf), zzz501, ty_Ordering, gf)
new_splitGT24(zzz79, zzz80, zzz81, zzz82, db) → new_mkVBalBranch3(zzz79, new_splitGT18(zzz81, db), zzz82, db)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_splitLT16(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT29(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Zero, ec)
new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_addToFM_C3(Branch(LT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → Branch(LT, new_addToFM0(zzz3191, zzz41, bb), zzz3192, zzz3193, zzz3194)
new_splitGT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_addToFM1(zzz44, zzz41, bb) → new_addToFM_C2(zzz44, zzz41, bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), gc) → new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, gc)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ge) → new_mkVBalBranch3MkVBalBranch285(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), fd) → new_mkBalBranch(zzz1350, zzz1351, zzz1353, new_mkVBalBranch2(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), fd), ty_Ordering, fd)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Succ(zzz18660000)))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ee)
new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), eg)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT9(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1970, dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, zzz1970, zzz196100, dh, ea)
new_mkVBalBranch3MkVBalBranch290(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb) → new_mkVBalBranch3MkVBalBranch289(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_splitLT16(EmptyFM, be) → new_splitLT42(be)
new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca) → new_mkVBalBranch3(zzz902, new_splitGT19(zzz904, ca), zzz905, ca)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), eb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), fc) → new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, fc)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch256(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, Branch(zzz14753430, zzz14753431, zzz14753432, zzz14753433, zzz14753434), zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz14753430, zzz14753431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz147530, zzz147531, zzz1836, zzz14753433, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz1475340, zzz1475341, zzz14753434, zzz1475344, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1761, Branch(zzz1756, zzz1757, Pos(Succ(zzz1758)), zzz1759, zzz1760), Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), fb) → new_mkBalBranch(zzz548, zzz549, new_mkVBalBranch3(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, fb), zzz552, ty_Ordering, fb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitLT16(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_splitGT15(zzz441, zzz442, zzz443, zzz444, bb)
new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20060), dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1966, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), gg) → new_mkBalBranch(zzz1843, zzz1844, zzz1846, new_mkVBalBranch3(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), gg), ty_Ordering, gg)
new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitGT211(zzz886, zzz887, zzz888, zzz889, be)
new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_splitLT17(Branch(LT, zzz811, zzz812, zzz813, zzz814), db) → new_mkVBalBranch2(zzz811, zzz813, new_splitLT17(zzz814, db), db)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz18360, zzz18361, zzz18363, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz147530, zzz147531, zzz18364, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Zero))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz186600)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, gh) → new_mkVBalBranch3MkVBalBranch251(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT10(zzz441, zzz442, zzz443, bb), bb)
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), ga, gb) → zzz13792
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), gc)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch289(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitGT211(zzz886, zzz887, zzz888, zzz889, be) → new_mkVBalBranch4(zzz886, new_splitGT19(zzz888, be), zzz889, be)
new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_addToFM_C4(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(EQ, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), bb)
new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2004, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT15(bb) → new_splitLT42(bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_primPlusInt(zzz13430, Neg(zzz14600)) → new_primMinusNat0(zzz13430, zzz14600)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20380), dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz20380, dh, ea)
new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, zzz1959, dh, ea) → new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz1959, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20110), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz20110, dh, ea)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ge) → new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ge)
new_splitLT17(Branch(EQ, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT27(zzz811, zzz812, zzz813, zzz814, db)
new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitLT42(bb) → new_emptyFM(bb)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20090), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_emptyFM(h) → EmptyFM
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), ff) → new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, ff)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_splitGT6(bb) → new_splitGT41(bb)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_splitLT17(EmptyFM, db) → new_splitLT41(db)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, bb)
new_splitGT18(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT29(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), ef) → new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, ef)
new_primPlusNat3(Zero) → Zero
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), ec) → new_mkBalBranch(zzz1020, zzz1021, new_mkVBalBranch2(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, ec), zzz1024, ty_Ordering, ec)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), gd) → new_mkBalBranch(zzz977, zzz978, new_mkVBalBranch3(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, gd), zzz981, ty_Ordering, gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), gd)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_primMinusNat0(Zero, Succ(zzz642000)) → Neg(Succ(zzz642000))
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Zero, eh)
new_splitGT5(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT16(bb), zzz44, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_primPlusInt1(zzz13430, Neg(zzz14650)) → Neg(new_primPlusNat2(zzz13430, zzz14650))
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), fd) → new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, fd)
new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_primPlusNat2(Zero, Zero) → Zero
new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_splitLT24(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT23(zzz79, zzz80, zzz81, zzz82, db)
new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1355, Branch(zzz1350, zzz1351, Pos(Succ(zzz1352)), zzz1353, zzz1354), Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), ty_Ordering, fd)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20390), dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, Branch(zzz18360, zzz18361, zzz18362, zzz18363, zzz18364), zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_sizeFM(zzz18364, dh, ea), new_sizeFM(zzz18363, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_splitLT5(zzz41, zzz42, zzz44, bb) → new_splitLT15(bb)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19710), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkBranch(zzz2030, zzz2031, zzz2032, zzz2033, zzz2034, fg, fh) → Branch(zzz2031, zzz2032, new_primPlusInt0(new_primPlusInt(Succ(Zero), new_sizeFM(zzz2033, fg, fh)), zzz2034, zzz2031, zzz2033, fg, fh), zzz2033, zzz2034)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb)
new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ge) → new_mkBalBranch(zzz1114, zzz1115, new_mkVBalBranch4(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ge), zzz1118, ty_Ordering, ge)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec) → new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), ec)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), eh)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_addToFM_C3(EmptyFM, zzz41, bb) → Branch(LT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), gh) → new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, gh)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19700), zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz19700, zzz196100, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20160), zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20160, zzz199000, dh, ea)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch251(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg)
new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce)
new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_splitGT17(bb) → new_splitGT42(bb)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Zero, ef)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, bb)
new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1848, Branch(zzz1843, zzz1844, Pos(Succ(zzz1845)), zzz1846, zzz1847), Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_splitLT41(bb) → new_emptyFM(bb)
new_splitGT19(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT211(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT10(zzz41, zzz42, zzz43, bb) → new_splitGT17(bb)
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, gh) → new_mkVBalBranch3MkVBalBranch252(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_splitLT12(EmptyFM, df) → new_splitLT40(df)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_splitLT29(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT16(zzz888, be)
new_intersectFM_C2Gts0(zzz1993, df) → new_splitGT12(zzz1993, df)
new_mkVBalBranch4(zzz41, EmptyFM, zzz44, bb) → new_addToFM1(zzz44, zzz41, bb)
new_addToFM_C3(Branch(GT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(GT, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), zzz199000, dh, ea)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), ha) → new_mkBalBranch(zzz952, zzz953, new_mkVBalBranch4(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, ha), zzz956, ty_Ordering, ha)
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, ha) → new_mkVBalBranch3MkVBalBranch290(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2040, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), bb)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, Branch(zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344), dh, ea) → new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_sizeFM(zzz1475343, dh, ea), new_sizeFM(zzz1475344, dh, ea), dh, ea)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_splitLT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT24(zzz79, zzz80, zzz81, zzz82, db)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_splitLT16(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_addToFM(zzz44, zzz41, bb) → new_addToFM_C4(zzz44, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_addToFM_C2(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(EQ, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Zero, eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Zero, eg)
new_primMinusNat0(Succ(zzz94600), Succ(zzz642000)) → new_primMinusNat0(zzz94600, zzz642000)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch281(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT18(x0)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT14(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT19(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT41(x0)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primMulNat0(x0)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch269(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_primPlusNat2(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Zero, x5, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_splitGT8(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_splitGT16(x0)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch30(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT16(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch292(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Zero, Zero)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_addToFM1(x0, x1, x2)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5)
new_primPlusNat1(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primPlusInt(x0, Neg(x1))
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(EmptyFM, x0, x1)
new_splitGT211(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Gts0(x0, x1)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT17(EmptyFM, x0)
new_splitLT6(x0)
new_splitLT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_splitGT18(Branch(LT, x0, x1, x2, x3), x4)
new_splitGT19(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch284(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT4(x0, x1, x2, x3)
new_primMulNat(Zero)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_primPlusInt(x0, Pos(x1))
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_primPlusInt0(Pos(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusInt1(x0, Pos(x1))
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
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_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitLT23(x0, x1, x2, x3, x4)
new_splitGT15(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, x4, x5)
new_intersectFM_C2Lts3(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primMulNat1(x0)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_splitGT18(EmptyFM, x0)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_intersectFM_C2Gts3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT13(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitLT28(x0, x1, x2, x3, x4)
new_primPlusNat2(Succ(x0), Succ(x1))
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitLT16(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT17(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(x0)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT17(x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT14(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT16(EmptyFM, x0)
new_splitLT26(x0, x1, x2, x3, x4)
new_primPlusNat3(Succ(x0))
new_splitLT42(x0)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat2(Succ(x0))
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_intersectFM_C2Lts0(x0, x1)
new_addToFM2(x0, x1, x2)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT12(EmptyFM, x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitGT13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch273(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, Zero, x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_splitGT19(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch268(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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusNat3(Zero)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitLT16(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitGT42(x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitLT10(x0, x1, x2, x3)
new_splitGT18(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
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, Succ(x10), x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch261(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusNat1(x0, Zero)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_splitGT6(x0)
new_mkBalBranch6MkBalBranch30(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_emptyFM(x0)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch291(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(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_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_splitGT5(x0, x1, x2, x3)
new_primPlusInt0(Neg(x0), x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT17(Branch(GT, x0, x1, x2, x3), x4)
new_primPlusInt1(x0, Neg(x1))
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_splitLT17(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_addToFM(x0, x1, x2)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_splitGT24(x0, x1, x2, x3, x4)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT18(Branch(GT, x0, x1, x2, x3), x4)
new_splitGT7(x0, x1, x2, x3, x4)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch171(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, x10, x11)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_primMulNat(Succ(x0))
new_splitLT27(x0, x1, x2, x3, x4)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch267(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_sizeFM(EmptyFM, x0, x1)
new_splitGT19(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)

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

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

new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, GT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz914, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C15(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, LT, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz930, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz43331, zzz43332, zzz43333, zzz43334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444)), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C11(zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444), zzz3, zzz51, zzz52, zzz53, zzz54, zzz440, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, GT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz898, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT6(bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, EmptyFM))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT11(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT23(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT8(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(EQ, zzz41, zzz42, zzz43, zzz44), zzz3, zzz51, zzz52, zzz53, zzz54, zzz41, zzz42, zzz43, zzz44, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT5(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, EmptyFM, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT8(zzz431, zzz432, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz4331, zzz4332, zzz4333, zzz4334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz4441, zzz4442, zzz4443, zzz4444, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C10(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz431, zzz432, zzz433, zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz44441, zzz44442, zzz44443, zzz44444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C16(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C13(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT10(zzz41, zzz42, zzz43, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), zzz3, zzz51, zzz52, zzz53, zzz54, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT4(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz44441, zzz44442, zzz44443, zzz44444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, EmptyFM)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT7(zzz431, zzz432, zzz433, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C13(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C14(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444441, zzz444442, zzz444443, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C15(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT24(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)

The TRS R consists of the following rules:

new_intersectFM_C2Gts0(zzz1993, df) → new_splitGT12(zzz1993, df)
new_splitGT12(EmptyFM, df) → new_splitGT42(df)
new_splitGT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT27(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_splitGT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_splitGT42(bb) → new_emptyFM(bb)
new_emptyFM(h) → EmptyFM
new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb)
new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb) → new_splitGT14(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb)
new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_splitGT15(zzz441, zzz442, zzz443, zzz444, bb)
new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT9(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT29(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT29(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT24(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT24(zzz79, zzz80, zzz81, zzz82, db) → new_mkVBalBranch3(zzz79, new_splitGT18(zzz81, db), zzz82, db)
new_splitGT18(Branch(EQ, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT210(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_splitGT18(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT26(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT18(zzz920, ce)
new_splitGT18(EmptyFM, ce) → new_splitGT41(ce)
new_splitGT18(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT29(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, zzz552, zzz553, zzz554), EmptyFM, bb) → new_addToFM(Branch(zzz550, zzz551, zzz552, zzz553, zzz554), zzz41, bb)
new_mkVBalBranch3(zzz41, EmptyFM, zzz44, bb) → new_addToFM(zzz44, zzz41, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBranch(zzz2030, zzz2031, zzz2032, zzz2033, zzz2034, fg, fh) → Branch(zzz2031, zzz2032, new_primPlusInt0(new_primPlusInt(Succ(Zero), new_sizeFM(zzz2033, fg, fh)), zzz2034, zzz2031, zzz2033, fg, fh), zzz2033, zzz2034)
new_sizeFM(EmptyFM, ga, gb) → Pos(Zero)
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), ga, gb) → zzz13792
new_primPlusInt(zzz13430, Pos(zzz14600)) → Pos(new_primPlusNat2(zzz13430, zzz14600))
new_primPlusInt(zzz13430, Neg(zzz14600)) → new_primMinusNat0(zzz13430, zzz14600)
new_primPlusInt0(Pos(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_primPlusInt0(Neg(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt1(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_primPlusInt1(zzz13430, Pos(zzz14650)) → new_primMinusNat0(zzz14650, zzz13430)
new_primPlusInt1(zzz13430, Neg(zzz14650)) → Neg(new_primPlusNat2(zzz13430, zzz14650))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Zero) → Zero
new_primMinusNat0(Succ(zzz94600), Zero) → Pos(Succ(zzz94600))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz642000)) → Neg(Succ(zzz642000))
new_primMinusNat0(Succ(zzz94600), Succ(zzz642000)) → new_primMinusNat0(zzz94600, zzz642000)
new_mkBalBranch(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, new_primPlusInt2(new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz1836, dh, ea)
new_primPlusInt2(Neg(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt1(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_primPlusInt2(Pos(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Zero)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Succ(zzz18660000)))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Zero))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz186600)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Zero, zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, zzz1959, dh, ea) → new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz1959, dh, ea)
new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19670), dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz19670, dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20050), dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz20050, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Succ(Zero), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2008, dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, zzz2008, zzz198800, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20080), zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz20080, zzz198800, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz1988000, zzz200300, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, EmptyFM, zzz147534, dh, ea) → error([])
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, Branch(zzz18360, zzz18361, zzz18362, zzz18363, zzz18364), zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_sizeFM(zzz18364, dh, ea), new_sizeFM(zzz18363, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_primMulNat2(Succ(zzz199100)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz199100)), Succ(zzz199100))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2040, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz18360, zzz18361, zzz18363, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz147530, zzz147531, zzz18364, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20390), dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, EmptyFM, zzz147534, dh, ea) → error([])
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, Branch(zzz183640, zzz183641, zzz183642, zzz183643, zzz183644), zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz183640, zzz183641, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz18360, zzz18361, zzz18363, zzz183643, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz147530, zzz147531, zzz183644, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2041, dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2041, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20410), zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20410, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2027000, zzz203500, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20380), dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz20380, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20430), dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20430, Zero, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2036, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20420), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Succ(zzz20350), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz20350, dh, ea)
new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2004, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20100), dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz20100, Zero, dh, ea)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20060), dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2007, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20090), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Succ(zzz20030), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz20030, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat3(Zero) → Zero
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19720), dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz19720, Zero, dh, ea)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, EmptyFM, dh, ea) → error([])
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, Branch(zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344), dh, ea) → new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_sizeFM(zzz1475343, dh, ea), new_sizeFM(zzz1475344, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), zzz199000, dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20160), zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20160, zzz199000, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz1990000, zzz201500, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, EmptyFM, zzz1475344, dh, ea) → error([])
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, Branch(zzz14753430, zzz14753431, zzz14753432, zzz14753433, zzz14753434), zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz14753430, zzz14753431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz147530, zzz147531, zzz1836, zzz14753433, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz1475340, zzz1475341, zzz14753434, zzz1475344, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Zero)), zzz1475340, zzz1475341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz147530, zzz147531, zzz1836, zzz1475343, dh, ea), zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20130), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20140), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20140, Zero, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20110), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz20110, dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Succ(zzz20150), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, zzz20150, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20120), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1970, dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, zzz1970, zzz196100, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19700), zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz19700, zzz196100, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz1961000, zzz196500, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19680), dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1966, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1969, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19710), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Succ(zzz19650), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz19650, dh, ea)
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), gd) → new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, gd)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd) → new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), gd)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), gg) → new_mkBalBranch(zzz1843, zzz1844, zzz1846, new_mkVBalBranch3(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), gg), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), gg) → new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1848, Branch(zzz1843, zzz1844, Pos(Succ(zzz1845)), zzz1846, zzz1847), Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), gd) → new_mkBalBranch(zzz977, zzz978, new_mkVBalBranch3(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, gd), zzz981, ty_Ordering, gd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch251(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), gh) → new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), gh) → new_mkBalBranch(zzz1159, zzz1160, new_mkVBalBranch3(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, gh), zzz1163, ty_Ordering, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, gh) → new_mkVBalBranch3MkVBalBranch251(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, gh) → new_mkVBalBranch3MkVBalBranch252(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), eg)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), eg)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Zero, eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Zero, eg)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1697, Branch(zzz1692, zzz1693, Neg(Succ(zzz1694)), zzz1695, zzz1696), Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), ff) → new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), ff) → new_mkBalBranch(zzz1692, zzz1693, zzz1695, new_mkVBalBranch3(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ff), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch3MkVBalBranch251(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg)
new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), fb) → new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), fb) → new_mkBalBranch(zzz548, zzz549, new_mkVBalBranch3(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, fb), zzz552, ty_Ordering, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb) → new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), fb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), fb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Zero, fb)
new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch147(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_addToFM(zzz44, zzz41, bb) → new_addToFM_C4(zzz44, zzz41, bb)
new_addToFM_C4(EmptyFM, zzz41, bb) → Branch(GT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C4(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(GT, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_addToFM_C4(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM_C4(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(EQ, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM0(zzz441, zzz41, bb) → zzz41
new_splitGT41(bb) → new_emptyFM(bb)
new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitLT17(Branch(LT, zzz917, zzz918, zzz919, zzz920), ce)
new_splitLT17(Branch(LT, zzz811, zzz812, zzz813, zzz814), db) → new_mkVBalBranch2(zzz811, zzz813, new_splitLT17(zzz814, db), db)
new_splitLT23(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT17(zzz81, db)
new_splitLT24(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT23(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT17(Branch(GT, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT24(zzz811, zzz812, zzz813, zzz814, db)
new_splitLT17(Branch(EQ, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT27(zzz811, zzz812, zzz813, zzz814, db)
new_splitLT17(EmptyFM, db) → new_splitLT41(db)
new_mkVBalBranch2(zzz41, EmptyFM, zzz319, bb) → new_addToFM2(zzz319, zzz41, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), EmptyFM, bb) → new_addToFM2(Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz41, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), gc) → new_mkBalBranch(zzz1006, zzz1007, new_mkVBalBranch2(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, gc), zzz1010, ty_Ordering, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), gc) → new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc) → new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), gc)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), fd) → new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), fd) → new_mkBalBranch(zzz1350, zzz1351, zzz1353, new_mkVBalBranch2(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), fd), ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1355, Branch(zzz1350, zzz1351, Pos(Succ(zzz1352)), zzz1353, zzz1354), Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), ec) → new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), ec) → new_mkBalBranch(zzz1020, zzz1021, new_mkVBalBranch2(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, ec), zzz1024, ty_Ordering, ec)
new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec) → new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), ec)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), ec)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Zero, ec)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1369, Branch(zzz1364, zzz1365, Neg(Succ(zzz1366)), zzz1367, zzz1368), Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), fc) → new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), fc) → new_mkBalBranch(zzz1364, zzz1365, zzz1367, new_mkVBalBranch2(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), fc), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_addToFM2(zzz319, zzz41, bb) → new_addToFM_C3(zzz319, zzz41, bb)
new_addToFM_C3(Branch(EQ, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(EQ, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_addToFM_C3(Branch(LT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → Branch(LT, new_addToFM0(zzz3191, zzz41, bb), zzz3192, zzz3193, zzz3194)
new_addToFM_C3(EmptyFM, zzz41, bb) → Branch(LT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C3(Branch(GT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(GT, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_splitLT41(bb) → new_emptyFM(bb)
new_splitGT4(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch4(zzz41, new_splitGT16(bb), zzz44, bb)
new_splitGT16(bb) → new_splitGT40(bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, zzz542, zzz543, zzz544), EmptyFM, bb) → new_addToFM1(Branch(zzz540, zzz541, zzz542, zzz543, zzz544), zzz41, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch4(zzz41, EmptyFM, zzz44, bb) → new_addToFM1(zzz44, zzz41, bb)
new_addToFM1(zzz44, zzz41, bb) → new_addToFM_C2(zzz44, zzz41, bb)
new_addToFM_C2(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(GT, zzz441, new_addToFM_C2(zzz443, zzz41, bb), zzz444, ty_Ordering, bb)
new_addToFM_C2(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C2(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM_C2(EmptyFM, zzz41, bb) → Branch(EQ, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C2(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(EQ, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch290(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch284(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ge) → new_mkVBalBranch3MkVBalBranch284(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ge) → new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ge) → new_mkVBalBranch3MkVBalBranch285(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ge) → new_mkBalBranch(zzz1114, zzz1115, new_mkVBalBranch4(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ge), zzz1118, ty_Ordering, ge)
new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), eb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), ed) → new_mkBalBranch(zzz1756, zzz1757, zzz1759, new_mkVBalBranch4(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ed), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), ed) → new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1761, Branch(zzz1756, zzz1757, Pos(Succ(zzz1758)), zzz1759, zzz1760), Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch284(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), ha) → new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, ha)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, ha) → new_mkVBalBranch3MkVBalBranch289(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkVBalBranch3MkVBalBranch289(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ee)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), ha) → new_mkBalBranch(zzz952, zzz953, new_mkVBalBranch4(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, ha), zzz956, ty_Ordering, ha)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, ha) → new_mkVBalBranch3MkVBalBranch290(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkVBalBranch3MkVBalBranch290(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb) → new_mkVBalBranch3MkVBalBranch289(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb)
new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch256(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), ef)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Zero, ef)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1862, Branch(zzz1857, zzz1858, Neg(Succ(zzz1859)), zzz1860, zzz1861), Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), fa) → new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), fa) → new_mkBalBranch(zzz1857, zzz1858, zzz1860, new_mkVBalBranch4(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), fa), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch256(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch256(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, gf) → new_mkBalBranch(zzz497, zzz498, new_mkVBalBranch4(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, gf), zzz501, ty_Ordering, gf)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef) → new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), ef)
new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, eh)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh) → new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), eh)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Zero, eh)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), eh)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), ef) → new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, ef)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), ef) → new_mkBalBranch(zzz509, zzz510, new_mkVBalBranch4(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, ef), zzz513, ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_splitGT40(bb) → new_emptyFM(bb)
new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb)
new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT9(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT24(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT14(zzz441, zzz442, zzz443, zzz444, bb), bb)
new_splitLT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch2(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_splitLT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitLT26(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_splitLT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch4(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_splitLT12(EmptyFM, df) → new_splitLT40(df)
new_splitLT40(bb) → new_emptyFM(bb)
new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb)
new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca)
new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca) → new_mkVBalBranch3(zzz902, new_splitGT19(zzz904, ca), zzz905, ca)
new_splitGT19(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT19(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT19(EmptyFM, be) → new_splitGT40(be)
new_splitGT19(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT211(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT211(zzz886, zzz887, zzz888, zzz889, be) → new_mkVBalBranch4(zzz886, new_splitGT19(zzz888, be), zzz889, be)
new_splitGT8(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT6(bb), zzz44, bb)
new_splitGT6(bb) → new_splitGT41(bb)
new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT16(zzz904, ca)
new_splitLT29(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT16(zzz888, be)
new_splitLT16(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT29(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT16(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT16(EmptyFM, be) → new_splitLT42(be)
new_splitLT16(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitLT42(bb) → new_emptyFM(bb)
new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT29(zzz886, zzz887, zzz888, zzz889, be)
new_intersectFM_C2Lts0(zzz1993, df) → new_splitLT12(zzz1993, df)
new_splitLT10(zzz41, zzz42, zzz43, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT18(bb), bb)
new_splitLT18(bb) → new_splitLT40(bb)
new_splitGT5(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT16(bb), zzz44, bb)
new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce)
new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitGT211(zzz886, zzz887, zzz888, zzz889, be)
new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT10(zzz441, zzz442, zzz443, bb), bb)
new_splitLT6(bb) → new_splitLT41(bb)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch281(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT18(x0)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT14(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT19(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT41(x0)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primMulNat0(x0)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch269(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_primPlusNat2(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Zero, x5, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_splitLT8(x0, x1, x2, x3)
new_splitGT8(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_splitGT16(x0)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch30(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT16(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch292(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Zero, Zero)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_addToFM1(x0, x1, x2)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5)
new_primPlusNat1(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primPlusInt(x0, Neg(x1))
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(EmptyFM, x0, x1)
new_splitGT211(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Gts0(x0, x1)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT17(EmptyFM, x0)
new_splitLT6(x0)
new_splitLT5(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_splitGT18(Branch(LT, x0, x1, x2, x3), x4)
new_splitGT19(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch284(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT4(x0, x1, x2, x3)
new_primMulNat(Zero)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_primPlusInt(x0, Pos(x1))
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_primPlusInt0(Pos(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusInt1(x0, Pos(x1))
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
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_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitLT23(x0, x1, x2, x3, x4)
new_splitGT15(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, x4, x5)
new_intersectFM_C2Lts3(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primMulNat1(x0)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_splitGT18(EmptyFM, x0)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_intersectFM_C2Gts3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT13(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitLT28(x0, x1, x2, x3, x4)
new_primPlusNat2(Succ(x0), Succ(x1))
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitLT16(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT17(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT15(x0)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT17(x0)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT14(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT16(EmptyFM, x0)
new_splitLT26(x0, x1, x2, x3, x4)
new_primPlusNat3(Succ(x0))
new_splitLT42(x0)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat2(Succ(x0))
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_intersectFM_C2Lts0(x0, x1)
new_addToFM2(x0, x1, x2)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT12(EmptyFM, x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitGT13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT4(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch273(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, Zero, x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_splitGT19(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch268(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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusNat3(Zero)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitLT16(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitGT42(x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitLT10(x0, x1, x2, x3)
new_splitGT18(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
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, Succ(x10), x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch261(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusNat1(x0, Zero)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_splitGT10(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_splitGT6(x0)
new_mkBalBranch6MkBalBranch30(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_emptyFM(x0)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch291(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(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_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_splitGT5(x0, x1, x2, x3)
new_primPlusInt0(Neg(x0), x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT17(Branch(GT, x0, x1, x2, x3), x4)
new_primPlusInt1(x0, Neg(x1))
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_splitLT17(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_addToFM(x0, x1, x2)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_splitGT24(x0, x1, x2, x3, x4)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT18(Branch(GT, x0, x1, x2, x3), x4)
new_splitGT7(x0, x1, x2, x3, x4)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch171(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, x10, x11)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_primMulNat(Succ(x0))
new_splitLT27(x0, x1, x2, x3, x4)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch267(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_sizeFM(EmptyFM, x0, x1)
new_splitGT19(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)

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_splitLT8(x0, x1, x2, x3)
new_splitLT5(x0, x1, x2, x3)
new_splitGT11(x0, x1, x2, x3, x4, x5, x6)
new_splitLT15(x0)
new_splitGT17(x0)
new_splitLT4(x0, x1, x2, x3)
new_splitGT10(x0, x1, x2, x3)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ IFR
            ↳ HASKELL
              ↳ BR
                ↳ HASKELL
                  ↳ COR
                    ↳ HASKELL
                      ↳ LetRed
                        ↳ HASKELL
                          ↳ NumRed
                            ↳ HASKELL
                              ↳ Narrow
                                ↳ AND
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ QDP
                                  ↳ 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(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, GT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz914, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C1(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C15(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, LT, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz930, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), zzz930, cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(LT, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz43331, zzz43332, zzz43333, zzz43334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444)), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C11(zzz41, zzz42, zzz43, Branch(zzz440, zzz441, zzz442, zzz443, zzz444), zzz3, zzz51, zzz52, zzz53, zzz54, zzz440, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EmptyFM, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, GT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz898, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(GT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca), zzz909, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT6(bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EmptyFM, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, EmptyFM))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT11(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT23(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(EQ, zzz41, zzz42, zzz43, zzz44), zzz3, zzz51, zzz52, zzz53, zzz54, zzz41, zzz42, zzz43, zzz44, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT8(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT5(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, EmptyFM, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT8(zzz431, zzz432, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(LT, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz4331, zzz4332, zzz4333, zzz4334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, LT, zzz896, zzz897, zzz898, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be), zzz894, bc, bd, be)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(EQ, zzz4441, zzz4442, zzz4443, zzz4444))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz4441, zzz4442, zzz4443, zzz4444, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C10(zzz41, zzz42, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz430, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, Branch(zzz9290, zzz9291, zzz9292, zzz9293, zzz9294), cc, cd, ce, cf) → new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, zzz9290, zzz9291, zzz9292, zzz9293, zzz9294, cc, cd, ce, cf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz431, zzz432, zzz433, zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, zzz43, zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(EQ, zzz44441, zzz44442, zzz44443, zzz44444)))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz44441, zzz44442, zzz44443, zzz44444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(EQ, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20021, zzz20022, zzz20023, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C16(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(LT, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), zzz899, bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(GT, zzz4441, zzz4442, zzz4443, zzz4444))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C13(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(LT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, Branch(GT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz913, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Lts0(zzz1993, df), zzz1997, dd, de, df)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, LT, zzz912, zzz913, zzz914, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C2IntersectFM_C111(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, EmptyFM, zzz915, bg, bh, ca, cb) → new_intersectFM_C(zzz906, new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca), zzz910, bg, bh, ca)
new_intersectFM_C2IntersectFM_C17(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz1999, zzz2000, zzz2001, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, GT, zzz927, zzz928, EmptyFM, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(EQ, zzz43331, zzz43332, zzz43333, zzz43334), zzz4334), zzz434), zzz44, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, EmptyFM), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT10(zzz41, zzz42, zzz43, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(EQ, zzz441, zzz442, zzz443, zzz444)), zzz3, zzz51, zzz52, zzz53, zzz54, zzz441, zzz442, zzz443, zzz444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C19(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C(zzz3, Branch(EQ, zzz41, zzz42, EmptyFM, zzz44), Branch(LT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT4(zzz41, zzz42, zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C14(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db), zzz86, cg, da, db)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C12(zzz41, zzz42, Branch(LT, zzz431, zzz432, zzz433, zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz431, zzz432, zzz433, zzz434, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(LT, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, EmptyFM))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, Branch(LT, zzz20021, zzz20022, zzz20023, zzz20024), dd, de, df, dg) → new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, zzz20024, dd, de, df, dg)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT13(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz44441, zzz44442, zzz44443, zzz44444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, EmptyFM)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, EQ, zzz912, zzz913, Branch(zzz9140, zzz9141, zzz9142, zzz9143, zzz9144), zzz915, bg, bh, ca, cb) → new_intersectFM_C2IntersectFM_C10(zzz902, zzz903, zzz904, zzz905, zzz906, zzz907, zzz908, zzz909, zzz910, zzz9140, zzz9141, zzz9142, zzz9143, zzz9144, bg, bh, ca, cb)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Gts(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, EmptyFM, zzz43334), zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, Branch(EQ, zzz911, zzz912, zzz913, zzz914), cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz54, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(EQ, zzz431, zzz432, zzz433, zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch3(zzz41, new_splitGT7(zzz431, zzz432, zzz433, zzz434, bb), zzz44, bb), zzz54, h, ba, bb)
new_intersectFM_C2IntersectFM_C18(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, Branch(zzz8980, zzz8981, zzz8982, zzz8983, zzz8984), bc, bd, be, bf) → new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, zzz8980, zzz8981, zzz8982, zzz8983, zzz8984, bc, bd, be, bf)
new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz88, zzz89, zzz90, EmptyFM, cg, da, db, dc) → new_intersectFM_C(zzz83, new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db), zzz87, cg, da, db)
new_intersectFM_C2IntersectFM_C13(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc) → new_intersectFM_C2IntersectFM_C12(zzz79, zzz80, zzz81, zzz82, zzz83, zzz84, zzz85, zzz86, zzz87, zzz911, zzz912, zzz913, zzz914, cg, da, db, dc)
new_intersectFM_C2IntersectFM_C11(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EQ, zzz927, zzz928, zzz929, zzz930, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce), zzz924, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444)))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_mkVBalBranch2(zzz41, zzz43, new_splitLT12(Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(GT, zzz44441, zzz44442, zzz44443, zzz44444))), bb), bb), zzz53, h, ba, bb)
new_intersectFM_C2IntersectFM_C110(zzz917, zzz918, zzz919, zzz920, zzz921, zzz922, zzz923, zzz924, zzz925, EmptyFM, cc, cd, ce, cf) → new_intersectFM_C(zzz921, new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce), zzz925, cc, cd, ce)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C14(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(EQ, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C17(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(EQ, zzz444441, zzz444442, zzz444443, zzz444444))))), zzz3, zzz51, zzz52, zzz53, zzz54, zzz444441, zzz444442, zzz444443, zzz444444, h, ba, bb, bb)
new_intersectFM_C2IntersectFM_C1(zzz886, zzz887, zzz888, zzz889, zzz890, zzz891, zzz892, zzz893, zzz894, EQ, zzz896, zzz897, EmptyFM, zzz899, bc, bd, be, bf) → new_intersectFM_C(zzz890, new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be), zzz893, bc, bd, be)
new_intersectFM_C2IntersectFM_C16(zzz1993, zzz1994, zzz1995, zzz1996, zzz1997, zzz1998, EmptyFM, dd, de, df, dg) → new_intersectFM_C(zzz1994, new_intersectFM_C2Gts0(zzz1993, df), zzz1998, dd, de, df)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_intersectFM_C2Lts0(Branch(LT, zzz41, zzz42, zzz43, Branch(LT, zzz441, zzz442, zzz443, Branch(LT, zzz4441, zzz4442, zzz4443, Branch(LT, zzz44441, zzz44442, zzz44443, Branch(GT, zzz444441, zzz444442, zzz444443, zzz444444))))), bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C2IntersectFM_C15(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, Branch(GT, zzz43331, zzz43332, Branch(GT, zzz433331, zzz433332, zzz433333, zzz433334), zzz43334), zzz4334), zzz434), zzz44, zzz3, zzz51, zzz52, zzz53, zzz54, zzz433331, zzz433332, zzz433333, zzz433334, h, ba, bb, bb)
new_intersectFM_C(zzz3, Branch(LT, zzz41, zzz42, zzz43, Branch(GT, zzz441, zzz442, zzz443, zzz444)), Branch(GT, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitLT9(zzz431, zzz432, Branch(GT, zzz4331, zzz4332, EmptyFM, zzz4334), zzz434, bb), zzz53, h, ba, bb)
new_intersectFM_C(zzz3, Branch(GT, zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44), Branch(EQ, zzz51, zzz52, zzz53, zzz54), h, ba, bb) → new_intersectFM_C(zzz3, new_splitGT24(zzz41, zzz42, Branch(GT, zzz431, zzz432, Branch(EQ, zzz4331, zzz4332, zzz4333, zzz4334), zzz434), zzz44, bb), zzz54, h, ba, bb)

The TRS R consists of the following rules:

new_intersectFM_C2Gts0(zzz1993, df) → new_splitGT12(zzz1993, df)
new_splitGT12(EmptyFM, df) → new_splitGT42(df)
new_splitGT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT27(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_splitGT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitGT12(zzz19934, df)
new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_splitGT42(bb) → new_emptyFM(bb)
new_emptyFM(h) → EmptyFM
new_splitLT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb)
new_splitLT27(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitGT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb) → new_splitGT14(zzz441, zzz442, zzz443, zzz4441, zzz4442, zzz4443, zzz4444, bb)
new_splitGT14(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_splitGT15(zzz441, zzz442, zzz443, zzz444, bb)
new_splitGT15(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT27(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Gts(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT9(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT29(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT29(zzz79, zzz80, zzz81, zzz82, db) → new_splitGT24(zzz79, zzz80, zzz81, zzz82, db)
new_splitGT24(zzz79, zzz80, zzz81, zzz82, db) → new_mkVBalBranch3(zzz79, new_splitGT18(zzz81, db), zzz82, db)
new_splitGT18(Branch(EQ, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT210(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_splitGT18(Branch(LT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT26(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT18(zzz920, ce)
new_splitGT18(EmptyFM, ce) → new_splitGT41(ce)
new_splitGT18(Branch(GT, zzz9201, zzz9202, zzz9203, zzz9204), ce) → new_splitGT29(zzz9201, zzz9202, zzz9203, zzz9204, ce)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, zzz552, zzz553, zzz554), EmptyFM, bb) → new_addToFM(Branch(zzz550, zzz551, zzz552, zzz553, zzz554), zzz41, bb)
new_mkVBalBranch3(zzz41, EmptyFM, zzz44, bb) → new_addToFM(zzz44, zzz41, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Succ(zzz55200)), zzz553, zzz554), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, zzz442, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primMulNat0(zzz55200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkBranch(zzz2030, zzz2031, zzz2032, zzz2033, zzz2034, fg, fh) → Branch(zzz2031, zzz2032, new_primPlusInt0(new_primPlusInt(Succ(Zero), new_sizeFM(zzz2033, fg, fh)), zzz2034, zzz2031, zzz2033, fg, fh), zzz2033, zzz2034)
new_sizeFM(EmptyFM, ga, gb) → Pos(Zero)
new_sizeFM(Branch(zzz13790, zzz13791, zzz13792, zzz13793, zzz13794), ga, gb) → zzz13792
new_primPlusInt(zzz13430, Pos(zzz14600)) → Pos(new_primPlusNat2(zzz13430, zzz14600))
new_primPlusInt(zzz13430, Neg(zzz14600)) → new_primMinusNat0(zzz13430, zzz14600)
new_primPlusInt0(Pos(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_primPlusInt0(Neg(zzz20370), zzz2034, zzz2031, zzz2033, fg, fh) → new_primPlusInt1(zzz20370, new_sizeFM(zzz2034, fg, fh))
new_primPlusInt1(zzz13430, Pos(zzz14650)) → new_primMinusNat0(zzz14650, zzz13430)
new_primPlusInt1(zzz13430, Neg(zzz14650)) → Neg(new_primPlusNat2(zzz13430, zzz14650))
new_primPlusNat2(Succ(zzz940), Succ(zzz9500)) → Succ(Succ(new_primPlusNat2(zzz940, zzz9500)))
new_primPlusNat2(Zero, Succ(zzz9500)) → Succ(zzz9500)
new_primPlusNat2(Succ(zzz940), Zero) → Succ(zzz940)
new_primPlusNat2(Zero, Zero) → Zero
new_primMinusNat0(Succ(zzz94600), Zero) → Pos(Succ(zzz94600))
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_primMinusNat0(Zero, Succ(zzz642000)) → Neg(Succ(zzz642000))
new_primMinusNat0(Succ(zzz94600), Succ(zzz642000)) → new_primMinusNat0(zzz94600, zzz642000)
new_mkBalBranch(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, new_primPlusInt2(new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz1836, dh, ea)
new_primPlusInt2(Neg(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt1(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_primPlusInt2(Pos(zzz18680), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_primPlusInt(zzz18680, new_sizeFM(zzz147534, dh, ea))
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Zero)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Succ(zzz18660000)))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(Succ(Zero))), dh, ea) → new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz186600)), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch50(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), dh, ea) → new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch5(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Zero, zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch51(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch415(zzz147530, zzz147531, zzz1836, zzz147534, zzz1959, dh, ea) → new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), zzz1959, dh, ea)
new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_sizeFM(zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz196100)), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_mkBalBranch6MkBalBranch44(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19590), dh, ea) → new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19590), dh, ea)
new_primMulNat(Zero) → Zero
new_primMulNat(Succ(zzz148900)) → new_primPlusNat2(new_primMulNat0(zzz148900), Succ(zzz148900))
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19670), dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz19670, dh, ea)
new_mkBalBranch6MkBalBranch46(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, new_mkBalBranch6Size_l(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), new_mkBalBranch6Size_r(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Zero), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Neg(Succ(zzz198800)), Neg(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch39(zzz147530, zzz147531, zzz1836, zzz147534, Pos(Zero), Pos(zzz19890), dh, ea) → new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, new_primMulNat(zzz19890), dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch37(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20050), dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz20050, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBranch(Succ(Zero), zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch315(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch312(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2008, dh, ea) → new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, zzz2008, zzz198800, dh, ea)
new_mkBalBranch6MkBalBranch31(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20080), zzz198800, dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz20080, zzz198800, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz1988000, zzz200300, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz200300), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1988000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, EmptyFM, zzz147534, dh, ea) → error([])
new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, Branch(zzz18360, zzz18361, zzz18362, zzz18363, zzz18364), zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_sizeFM(zzz18364, dh, ea), new_sizeFM(zzz18363, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Pos(Zero), Neg(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, new_primMulNat2(zzz20280), dh, ea)
new_mkBalBranch6MkBalBranch112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Neg(Succ(zzz202700)), Pos(zzz20280), dh, ea) → new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, new_primMulNat2(zzz20280), dh, ea)
new_primMulNat2(Succ(zzz199100)) → new_primPlusNat2(new_primPlusNat2(Zero, Succ(zzz199100)), Succ(zzz199100))
new_primMulNat2(Zero) → Zero
new_mkBalBranch6MkBalBranch1112(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2040, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), zzz18360, zzz18361, zzz18363, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), zzz147530, zzz147531, zzz18364, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20390), dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch116(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, EmptyFM, zzz147534, dh, ea) → error([])
new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, Branch(zzz183640, zzz183641, zzz183642, zzz183643, zzz183644), zzz147534, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), zzz183640, zzz183641, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), zzz18360, zzz18361, zzz18363, zzz183643, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), zzz147530, zzz147531, zzz183644, zzz147534, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch117(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2041, dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2041, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20410), zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20410, zzz202700, dh, ea)
new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz202700, dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz2027000), Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz2027000, zzz203500, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, Succ(zzz203500), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch113(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20380), dh, ea) → new_mkBalBranch6MkBalBranch114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, zzz20380, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20430), dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz20430, Zero, dh, ea)
new_mkBalBranch6MkBalBranch1115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Zero, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2036, dh, ea) → new_mkBalBranch6MkBalBranch111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch115(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch1114(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, Succ(zzz20420), dh, ea) → new_mkBalBranch6MkBalBranch118(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch119(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea) → new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz2035, dh, ea)
new_mkBalBranch6MkBalBranch1110(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, Succ(zzz20350), dh, ea) → new_mkBalBranch6MkBalBranch1111(zzz147530, zzz147531, zzz18360, zzz18361, zzz18362, zzz18363, zzz18364, zzz147534, zzz202700, zzz20350, dh, ea)
new_mkBalBranch6MkBalBranch311(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2004, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch313(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20100), dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz20100, Zero, dh, ea)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Zero, dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20060), dh, ea) → new_mkBalBranch6MkBalBranch30(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch38(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch34(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2007, dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch36(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch35(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz20090), dh, ea) → new_mkBalBranch6MkBalBranch33(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch310(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea) → new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz2003, dh, ea)
new_mkBalBranch6MkBalBranch314(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, Succ(zzz20030), dh, ea) → new_mkBalBranch6MkBalBranch32(zzz147530, zzz147531, zzz1836, zzz147534, zzz198800, zzz20030, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Zero, zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea) → new_mkBalBranch6MkBalBranch412(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_primMulNat0(zzz7200) → new_primPlusNat1(Succ(new_primPlusNat1(new_primPlusNat3(zzz7200), zzz7200)), Succ(zzz7200))
new_primPlusNat3(Zero) → Zero
new_primPlusNat3(Succ(zzz72000)) → Succ(Succ(new_primPlusNat3(zzz72000)))
new_primPlusNat1(zzz94, Succ(zzz950)) → Succ(Succ(new_primPlusNat2(zzz94, zzz950)))
new_primPlusNat1(zzz94, Zero) → Succ(zzz94)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19720), dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz19720, Zero, dh, ea)
new_mkBalBranch6MkBalBranch410(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, EmptyFM, dh, ea) → error([])
new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, Branch(zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344), dh, ea) → new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_sizeFM(zzz1475343, dh, ea), new_sizeFM(zzz1475344, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Pos(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Zero), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Pos(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch016(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Neg(Succ(zzz199000)), Neg(zzz19910), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, new_primMulNat2(zzz19910), zzz199000, dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20160), zzz199000, dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20160, zzz199000, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz1990000, zzz201500, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz1990000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Succ(zzz201500), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, EmptyFM, zzz1475344, dh, ea) → error([])
new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, Branch(zzz14753430, zzz14753431, zzz14753432, zzz14753433, zzz14753434), zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), zzz14753430, zzz14753431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), zzz147530, zzz147531, zzz1836, zzz14753433, dh, ea), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), zzz1475340, zzz1475341, zzz14753434, zzz1475344, dh, ea), dh, ea)
new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBranch(Succ(Succ(Zero)), zzz1475340, zzz1475341, new_mkBranch(Succ(Succ(Succ(Zero))), zzz147530, zzz147531, zzz1836, zzz1475343, dh, ea), zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea) → new_mkBalBranch6MkBalBranch011(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20130), dh, ea) → new_mkBalBranch6MkBalBranch013(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch012(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20140), dh, ea) → new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz20140, Zero, dh, ea)
new_mkBalBranch6MkBalBranch0110(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Zero, dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch014(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20110), dh, ea) → new_mkBalBranch6MkBalBranch015(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, zzz20110, dh, ea)
new_mkBalBranch6MkBalBranch017(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, Succ(zzz20150), dh, ea) → new_mkBalBranch6MkBalBranch0111(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, zzz199000, zzz20150, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Succ(zzz20120), dh, ea) → new_mkBalBranch6MkBalBranch018(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch019(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, Zero, dh, ea) → new_mkBalBranch6MkBalBranch010(zzz147530, zzz147531, zzz1836, zzz1475340, zzz1475341, zzz1475342, zzz1475343, zzz1475344, dh, ea)
new_mkBalBranch6MkBalBranch48(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1970, dh, ea) → new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, zzz1970, zzz196100, dh, ea)
new_mkBalBranch6MkBalBranch414(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19700), zzz196100, dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz19700, zzz196100, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz1961000, zzz196500, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz1961000), Zero, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Succ(zzz196500), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, Zero, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch40(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19680), dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch43(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1966, dh, ea) → new_mkBalBranch6MkBalBranch41(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch47(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1969, dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Zero, dh, ea) → new_mkBalBranch6MkBalBranch42(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch49(zzz147530, zzz147531, zzz1836, zzz147534, Succ(zzz19710), dh, ea) → new_mkBalBranch6MkBalBranch411(zzz147530, zzz147531, zzz1836, zzz147534, dh, ea)
new_mkBalBranch6MkBalBranch45(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea) → new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz1965, dh, ea)
new_mkBalBranch6MkBalBranch413(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, Succ(zzz19650), dh, ea) → new_mkBalBranch6MkBalBranch416(zzz147530, zzz147531, zzz1836, zzz147534, zzz196100, zzz19650, dh, ea)
new_primMulNat1(zzz44200) → new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200))
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1340), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch162(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Neg(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, zzz55200, zzz44200, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch258(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(new_primPlusNat2(zzz710, zzz55200)), zzz44200, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz710), bb) → new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch257(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch259(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch260(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch161(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz1480), bb) → new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch172(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Succ(zzz9890), gd) → new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, zzz9880, zzz9890, gd)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz9880), Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd) → new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, new_primMulNat1(zzz979), gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Succ(zzz10510), Succ(zzz984), gd)
new_mkVBalBranch3MkVBalBranch167(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, gd) → new_mkVBalBranch3MkVBalBranch171(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz984), gd)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Succ(zzz18500), gg) → new_mkBalBranch(zzz1843, zzz1844, zzz1846, new_mkVBalBranch3(zzz1848, zzz1847, Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), gg), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Succ(zzz18500), gg) → new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, zzz18490, zzz18500, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Zero, Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch171(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, Succ(zzz18490), Zero, gg) → new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg)
new_mkVBalBranch3MkVBalBranch168(zzz1838, zzz1839, zzz1840, zzz1841, zzz1842, zzz1843, zzz1844, zzz1845, zzz1846, zzz1847, zzz1848, gg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1848, Branch(zzz1843, zzz1844, Pos(Succ(zzz1845)), zzz1846, zzz1847), Branch(zzz1838, zzz1839, Pos(Succ(zzz1840)), zzz1841, zzz1842), ty_Ordering, gg)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Zero, gd) → new_mkVBalBranch3MkVBalBranch282(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, gd)
new_mkVBalBranch3MkVBalBranch258(zzz977, zzz978, zzz979, zzz980, zzz981, zzz982, zzz983, zzz984, zzz985, zzz986, zzz987, Zero, Succ(zzz9890), gd) → new_mkBalBranch(zzz977, zzz978, new_mkVBalBranch3(zzz987, Branch(zzz982, zzz983, Pos(Succ(zzz984)), zzz985, zzz986), zzz980, gd), zzz981, ty_Ordering, gd)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch251(zzz440, zzz441, Zero, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Zero, Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, zzz442000, zzz552000, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz552000), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Succ(zzz552000), zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch273(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz552000, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7200, zzz552000))), bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, Succ(zzz720), bb) → new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch271(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz550, zzz551, Zero, zzz553, zzz554, zzz41, Succ(Succ(zzz7200)), bb) → new_mkVBalBranch3MkVBalBranch274(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz4420000), Succ(zzz7200), bb)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Succ(zzz11700), gh) → new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, zzz11690, zzz11700, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Succ(zzz11700), gh) → new_mkBalBranch(zzz1159, zzz1160, new_mkVBalBranch3(zzz1168, Branch(zzz1164, zzz1165, Neg(Succ(Zero)), zzz1166, zzz1167), zzz1162, gh), zzz1163, ty_Ordering, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Zero, Zero, gh) → new_mkVBalBranch3MkVBalBranch251(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkVBalBranch3MkVBalBranch274(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, Succ(zzz11690), Zero, gh) → new_mkVBalBranch3MkVBalBranch252(zzz1159, zzz1160, zzz1161, zzz1162, zzz1163, zzz1164, zzz1165, zzz1166, zzz1167, zzz1168, gh)
new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, new_primMulNat1(zzz852), eg)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Succ(zzz9310), eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Succ(zzz9310), eg)
new_mkVBalBranch3MkVBalBranch147(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, Zero, eg) → new_mkVBalBranch3MkVBalBranch145(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, Zero, zzz857, zzz858, zzz859, Succ(Zero), Zero, eg)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz1697, Branch(zzz1692, zzz1693, Neg(Succ(zzz1694)), zzz1695, zzz1696), Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Succ(zzz16980), Succ(zzz16990), ff) → new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, zzz16980, zzz16990, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Succ(zzz16990), ff) → new_mkBalBranch(zzz1692, zzz1693, zzz1695, new_mkVBalBranch3(zzz1697, zzz1696, Branch(zzz1687, zzz1688, Neg(Succ(zzz1689)), zzz1690, zzz1691), ff), ty_Ordering, ff)
new_mkVBalBranch3MkVBalBranch145(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, Zero, Zero, ff) → new_mkVBalBranch3MkVBalBranch154(zzz1687, zzz1688, zzz1689, zzz1690, zzz1691, zzz1692, zzz1693, zzz1694, zzz1695, zzz1696, zzz1697, ff)
new_mkVBalBranch3MkVBalBranch251(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg) → new_mkVBalBranch3MkVBalBranch252(zzz850, zzz851, zzz852, zzz853, zzz854, zzz855, zzz856, zzz857, zzz858, zzz859, eg)
new_mkVBalBranch3MkVBalBranch276(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch272(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Succ(zzz5600), fb) → new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, zzz5590, zzz5600, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz5590), Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Succ(zzz5600), fb) → new_mkBalBranch(zzz548, zzz549, new_mkVBalBranch3(zzz558, Branch(zzz553, zzz554, Neg(Succ(Succ(zzz555))), zzz556, zzz557), zzz551, fb), zzz552, ty_Ordering, fb)
new_mkVBalBranch3MkVBalBranch273(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, Zero, fb) → new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb)
new_mkVBalBranch3MkVBalBranch286(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, fb) → new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, new_primMulNat1(zzz550), fb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Succ(zzz7200), fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Succ(zzz7200), fb)
new_mkVBalBranch3MkVBalBranch144(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, zzz555, zzz556, zzz557, zzz558, Zero, fb) → new_mkVBalBranch3MkVBalBranch145(zzz548, zzz549, zzz550, zzz551, zzz552, zzz553, zzz554, Succ(zzz555), zzz556, zzz557, zzz558, Succ(Succ(zzz555)), Zero, fb)
new_mkVBalBranch3MkVBalBranch248(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb)
new_mkVBalBranch3MkVBalBranch249(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, bb) → new_mkVBalBranch3MkVBalBranch147(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkVBalBranch3MkVBalBranch275(zzz440, zzz441, zzz443, zzz444, zzz550, zzz551, zzz55200, zzz553, zzz554, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch3(zzz41, Branch(zzz550, zzz551, Neg(Succ(zzz55200)), zzz553, zzz554), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), GT, zzz41, Branch(zzz550, zzz551, Pos(Zero), zzz553, zzz554), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch158(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz550, zzz551, zzz553, zzz554, zzz41, Succ(zzz1300), bb) → new_mkBalBranch(zzz550, zzz551, zzz553, new_mkVBalBranch3(zzz41, zzz554, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_addToFM(zzz44, zzz41, bb) → new_addToFM_C4(zzz44, zzz41, bb)
new_addToFM_C4(EmptyFM, zzz41, bb) → Branch(GT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C4(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(GT, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_addToFM_C4(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM_C4(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(EQ, zzz441, zzz443, new_addToFM_C4(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM0(zzz441, zzz41, bb) → zzz41
new_splitGT41(bb) → new_emptyFM(bb)
new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_splitGT7(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT210(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Lts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitLT17(Branch(LT, zzz917, zzz918, zzz919, zzz920), ce)
new_splitLT17(Branch(LT, zzz811, zzz812, zzz813, zzz814), db) → new_mkVBalBranch2(zzz811, zzz813, new_splitLT17(zzz814, db), db)
new_splitLT23(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT17(zzz81, db)
new_splitLT24(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT23(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT17(Branch(GT, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT24(zzz811, zzz812, zzz813, zzz814, db)
new_splitLT17(Branch(EQ, zzz811, zzz812, zzz813, zzz814), db) → new_splitLT27(zzz811, zzz812, zzz813, zzz814, db)
new_splitLT17(EmptyFM, db) → new_splitLT41(db)
new_mkVBalBranch2(zzz41, EmptyFM, zzz319, bb) → new_addToFM2(zzz319, zzz41, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, zzz432, zzz433, zzz434), EmptyFM, bb) → new_addToFM2(Branch(zzz430, zzz431, zzz432, zzz433, zzz434), zzz41, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, zzz3192, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz43200), Succ(zzz43200)), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, new_primMulNat1(zzz319200), bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch159(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5610), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Pos(Zero), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch170(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz433, zzz434, zzz41, Succ(zzz5460), bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz4300, zzz319200, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch265(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, Succ(zzz319200), bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch264(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4300), bb) → new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch266(zzz3190, zzz3191, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Zero, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch267(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch247(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, new_primPlusNat2(new_primMulNat0(zzz319200), Succ(zzz319200)), bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch136(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz5730), bb) → new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch143(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz430, zzz431, zzz433, new_mkVBalBranch2(zzz41, zzz434, Branch(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz10180), gc) → new_mkBalBranch(zzz1006, zzz1007, new_mkVBalBranch2(zzz1016, Branch(zzz1011, zzz1012, Pos(Succ(zzz1013)), zzz1014, zzz1015), zzz1009, gc), zzz1010, ty_Ordering, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Succ(zzz10180), gc) → new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, zzz10170, zzz10180, gc)
new_mkVBalBranch3MkVBalBranch265(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10170), Zero, gc) → new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc)
new_mkVBalBranch3MkVBalBranch281(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, gc) → new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, new_primMulNat1(zzz1008), gc)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Zero, Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch166(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), gc) → new_mkVBalBranch3MkVBalBranch163(zzz1006, zzz1007, zzz1008, zzz1009, zzz1010, zzz1011, zzz1012, zzz1013, zzz1014, zzz1015, zzz1016, Succ(zzz10660), Succ(zzz1013), gc)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Succ(zzz13570), fd) → new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, zzz13560, zzz13570, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Zero, Succ(zzz13570), fd) → new_mkBalBranch(zzz1350, zzz1351, zzz1353, new_mkVBalBranch2(zzz1355, zzz1354, Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), fd), ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch163(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, Succ(zzz13560), Zero, fd) → new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd)
new_mkVBalBranch3MkVBalBranch148(zzz1345, zzz1346, zzz1347, zzz1348, zzz1349, zzz1350, zzz1351, zzz1352, zzz1353, zzz1354, zzz1355, fd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1355, Branch(zzz1350, zzz1351, Pos(Succ(zzz1352)), zzz1353, zzz1354), Branch(zzz1345, zzz1346, Pos(Succ(zzz1347)), zzz1348, zzz1349), ty_Ordering, fd)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Pos(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(zzz31920), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz319200), Zero, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Succ(zzz4320), bb) → new_mkVBalBranch3MkVBalBranch270(zzz3190, zzz3191, zzz319200, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, zzz319200, zzz4320, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), Branch(zzz3190, zzz3191, Neg(Zero), zzz3193, zzz3194), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch268(zzz3190, zzz3191, Pos(Succ(zzz319200)), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, Succ(zzz319200), zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb)
new_mkVBalBranch3MkVBalBranch269(zzz3190, zzz3191, zzz31920, zzz3193, zzz3194, zzz430, zzz431, zzz43200, zzz433, zzz434, zzz41, bb) → new_mkBalBranch(zzz3190, zzz3191, new_mkVBalBranch2(zzz41, Branch(zzz430, zzz431, Neg(Succ(zzz43200)), zzz433, zzz434), zzz3193, bb), zzz3194, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Succ(zzz10320), ec) → new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, zzz10310, zzz10320, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10310), Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Zero, ec) → new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec)
new_mkVBalBranch3MkVBalBranch270(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, Succ(zzz10320), ec) → new_mkBalBranch(zzz1020, zzz1021, new_mkVBalBranch2(zzz1030, Branch(zzz1025, zzz1026, Neg(Succ(zzz1027)), zzz1028, zzz1029), zzz1023, ec), zzz1024, ty_Ordering, ec)
new_mkVBalBranch3MkVBalBranch246(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, ec) → new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, new_primMulNat1(zzz1022), ec)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz10670), ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Succ(zzz10670), ec)
new_mkVBalBranch3MkVBalBranch135(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Zero, ec) → new_mkVBalBranch3MkVBalBranch141(zzz1020, zzz1021, zzz1022, zzz1023, zzz1024, zzz1025, zzz1026, zzz1027, zzz1028, zzz1029, zzz1030, Succ(zzz1027), Zero, ec)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), LT, zzz1369, Branch(zzz1364, zzz1365, Neg(Succ(zzz1366)), zzz1367, zzz1368), Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Succ(zzz13700), Succ(zzz13710), fc) → new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, zzz13700, zzz13710, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Succ(zzz13710), fc) → new_mkBalBranch(zzz1364, zzz1365, zzz1367, new_mkVBalBranch2(zzz1369, zzz1368, Branch(zzz1359, zzz1360, Neg(Succ(zzz1361)), zzz1362, zzz1363), fc), ty_Ordering, fc)
new_mkVBalBranch3MkVBalBranch141(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, Zero, Zero, fc) → new_mkVBalBranch3MkVBalBranch146(zzz1359, zzz1360, zzz1361, zzz1362, zzz1363, zzz1364, zzz1365, zzz1366, zzz1367, zzz1368, zzz1369, fc)
new_addToFM2(zzz319, zzz41, bb) → new_addToFM_C3(zzz319, zzz41, bb)
new_addToFM_C3(Branch(EQ, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(EQ, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_addToFM_C3(Branch(LT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → Branch(LT, new_addToFM0(zzz3191, zzz41, bb), zzz3192, zzz3193, zzz3194)
new_addToFM_C3(EmptyFM, zzz41, bb) → Branch(LT, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C3(Branch(GT, zzz3191, zzz3192, zzz3193, zzz3194), zzz41, bb) → new_mkBalBranch(GT, zzz3191, new_addToFM_C3(zzz3193, zzz41, bb), zzz3194, ty_Ordering, bb)
new_splitLT41(bb) → new_emptyFM(bb)
new_splitGT4(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch4(zzz41, new_splitGT16(bb), zzz44, bb)
new_splitGT16(bb) → new_splitGT40(bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, zzz542, zzz543, zzz544), EmptyFM, bb) → new_addToFM1(Branch(zzz540, zzz541, zzz542, zzz543, zzz544), zzz41, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(zzz44200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(zzz54200)), zzz543, zzz544), Branch(zzz440, zzz441, zzz442, zzz443, zzz444), bb) → new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, zzz442, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat0(zzz54200), bb)
new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Pos(Succ(zzz44200)), zzz443, zzz444), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch4(zzz41, EmptyFM, zzz44, bb) → new_addToFM1(zzz44, zzz41, bb)
new_addToFM1(zzz44, zzz41, bb) → new_addToFM_C2(zzz44, zzz41, bb)
new_addToFM_C2(Branch(GT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(GT, zzz441, new_addToFM_C2(zzz443, zzz41, bb), zzz444, ty_Ordering, bb)
new_addToFM_C2(Branch(LT, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → new_mkBalBranch(LT, zzz441, zzz443, new_addToFM_C2(zzz444, zzz41, bb), ty_Ordering, bb)
new_addToFM_C2(EmptyFM, zzz41, bb) → Branch(EQ, zzz41, Pos(Succ(Zero)), new_emptyFM(bb), new_emptyFM(bb))
new_addToFM_C2(Branch(EQ, zzz441, zzz442, zzz443, zzz444), zzz41, bb) → Branch(EQ, new_addToFM0(zzz441, zzz41, bb), zzz442, zzz443, zzz444)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz542000, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch290(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz542000), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch284(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch288(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz6900), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz690), bb) → new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Pos(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz6900)), bb) → new_mkVBalBranch3MkVBalBranch283(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(Succ(new_primPlusNat2(zzz6900, zzz542000))), zzz442000, bb)
new_mkVBalBranch3MkVBalBranch279(zzz440, zzz441, Neg(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch262(zzz440, zzz441, Succ(zzz44200), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primPlusNat2(new_primMulNat0(zzz44200), Succ(zzz44200)), bb)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1460), bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch151(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch157(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Zero, ge) → new_mkVBalBranch3MkVBalBranch284(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Succ(zzz11250), Succ(zzz11260), ge) → new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, zzz11250, zzz11260, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Zero, ge) → new_mkVBalBranch3MkVBalBranch285(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, ge)
new_mkVBalBranch3MkVBalBranch283(zzz1114, zzz1115, zzz1116, zzz1117, zzz1118, zzz1119, zzz1120, zzz1121, zzz1122, zzz1123, zzz1124, Zero, Succ(zzz11260), ge) → new_mkBalBranch(zzz1114, zzz1115, new_mkVBalBranch4(zzz1124, Branch(zzz1119, zzz1120, Pos(Succ(Succ(zzz1121))), zzz1122, zzz1123), zzz1117, ge), zzz1118, ty_Ordering, ge)
new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch152(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch153(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch164(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch133(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, new_primMulNat1(zzz476), eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Succ(zzz5990), eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Succ(zzz5990), Succ(Succ(zzz481)), eb)
new_mkVBalBranch3MkVBalBranch134(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, Zero, eb) → new_mkVBalBranch3MkVBalBranch137(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, Succ(zzz481), zzz482, zzz483, zzz484, Zero, Succ(Succ(zzz481)), eb)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Succ(zzz17630), ed) → new_mkBalBranch(zzz1756, zzz1757, zzz1759, new_mkVBalBranch4(zzz1761, zzz1760, Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ed), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Succ(zzz17630), ed) → new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, zzz17620, zzz17630, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Zero, Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch137(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, Succ(zzz17620), Zero, ed) → new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed)
new_mkVBalBranch3MkVBalBranch138(zzz1751, zzz1752, zzz1753, zzz1754, zzz1755, zzz1756, zzz1757, zzz1758, zzz1759, zzz1760, zzz1761, ed) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1761, Branch(zzz1756, zzz1757, Pos(Succ(zzz1758)), zzz1759, zzz1760), Branch(zzz1751, zzz1752, Pos(Succ(zzz1753)), zzz1754, zzz1755), ty_Ordering, ed)
new_mkVBalBranch3MkVBalBranch284(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb) → new_mkVBalBranch3MkVBalBranch285(zzz474, zzz475, zzz476, zzz477, zzz478, zzz479, zzz480, zzz481, zzz482, zzz483, zzz484, eb)
new_mkVBalBranch3MkVBalBranch291(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Pos(Zero), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Succ(zzz9630), ha) → new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, zzz9620, zzz9630, ha)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Succ(zzz9620), Zero, ha) → new_mkVBalBranch3MkVBalBranch289(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkVBalBranch3MkVBalBranch289(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch155(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee)
new_mkVBalBranch3MkVBalBranch156(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, ee) → new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, new_primMulNat1(zzz488), ee)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Zero, ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Zero, Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch139(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, zzz493, zzz494, zzz495, Succ(zzz7460), ee) → new_mkVBalBranch3MkVBalBranch137(zzz486, zzz487, zzz488, zzz489, zzz490, zzz491, zzz492, Zero, zzz493, zzz494, zzz495, Succ(zzz7460), Succ(Zero), ee)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Succ(zzz9630), ha) → new_mkBalBranch(zzz952, zzz953, new_mkVBalBranch4(zzz961, Branch(zzz957, zzz958, Pos(Succ(Zero)), zzz959, zzz960), zzz955, ha), zzz956, ty_Ordering, ha)
new_mkVBalBranch3MkVBalBranch288(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, Zero, Zero, ha) → new_mkVBalBranch3MkVBalBranch290(zzz952, zzz953, zzz954, zzz955, zzz956, zzz957, zzz958, zzz959, zzz960, zzz961, ha)
new_mkVBalBranch3MkVBalBranch290(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb) → new_mkVBalBranch3MkVBalBranch289(zzz814, zzz815, zzz816, zzz817, zzz818, zzz819, zzz820, zzz821, zzz822, zzz823, hb)
new_mkVBalBranch3MkVBalBranch261(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch149(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), bb) → new_mkVBalBranch3MkVBalBranch137(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz1530), Succ(zzz54200), bb)
new_mkVBalBranch3MkVBalBranch287(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Pos(Succ(Zero)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1250), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch165(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Pos(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch256(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Zero, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(zzz7000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Zero, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Zero), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, zzz442000, zzz542000, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Succ(zzz4420000)))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Succ(zzz4420000)), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Succ(zzz4420000), Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Pos(zzz4420), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Zero)), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(zzz542000), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch253(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, Zero, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(Zero))), zzz443, zzz444, zzz540, zzz541, Succ(zzz542000), zzz543, zzz544, zzz41, Succ(Succ(zzz7000)), bb) → new_mkVBalBranch3MkVBalBranch254(zzz440, zzz441, Succ(Zero), zzz443, zzz444, zzz540, zzz541, zzz542000, zzz543, zzz544, zzz41, Zero, Succ(Succ(new_primPlusNat2(zzz7000, zzz542000))), bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Succ(Succ(zzz442000))), zzz443, zzz444, zzz540, zzz541, Zero, zzz543, zzz544, zzz41, Zero, bb) → new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch280(zzz440, zzz441, Neg(Zero), zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, Succ(zzz700), bb) → new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch263(zzz440, zzz441, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch277(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb)
new_mkVBalBranch3MkVBalBranch278(zzz440, zzz441, zzz442000, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, bb) → new_mkVBalBranch3MkVBalBranch140(zzz440, zzz441, Succ(zzz442000), zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, new_primMulNat1(Succ(zzz442000)), bb)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz8360), ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Succ(zzz8360), ef)
new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, ef) → new_mkVBalBranch3MkVBalBranch169(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, Zero, zzz516, zzz517, zzz518, Succ(Zero), Zero, ef)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz1862, Branch(zzz1857, zzz1858, Neg(Succ(zzz1859)), zzz1860, zzz1861), Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Succ(zzz18630), Succ(zzz18640), fa) → new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, zzz18630, zzz18640, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Succ(zzz18640), fa) → new_mkBalBranch(zzz1857, zzz1858, zzz1860, new_mkVBalBranch4(zzz1862, zzz1861, Branch(zzz1852, zzz1853, Neg(Succ(zzz1854)), zzz1855, zzz1856), fa), ty_Ordering, fa)
new_mkVBalBranch3MkVBalBranch169(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, Zero, Zero, fa) → new_mkVBalBranch3MkVBalBranch142(zzz1852, zzz1853, zzz1854, zzz1855, zzz1856, zzz1857, zzz1858, zzz1859, zzz1860, zzz1861, zzz1862, fa)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch256(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch256(zzz497, zzz498, zzz499, zzz500, zzz501, zzz502, zzz503, zzz504, zzz505, zzz506, zzz507, gf) → new_mkBalBranch(zzz497, zzz498, new_mkVBalBranch4(zzz507, Branch(zzz502, zzz503, Neg(Succ(Succ(zzz504))), zzz505, zzz506), zzz500, gf), zzz501, ty_Ordering, gf)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef) → new_mkVBalBranch3MkVBalBranch140(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, new_primMulNat1(zzz511), ef)
new_mkVBalBranch3MkVBalBranch292(zzz440, zzz441, zzz4420, zzz443, zzz444, zzz540, zzz541, zzz54200, zzz543, zzz544, zzz41, bb) → new_mkBalBranch(zzz440, zzz441, new_mkVBalBranch4(zzz41, Branch(zzz540, zzz541, Neg(Succ(zzz54200)), zzz543, zzz544), zzz443, bb), zzz444, ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Succ(zzz11570), eh) → new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, zzz11560, zzz11570, eh)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch254(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz11560), Zero, eh) → new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh)
new_mkVBalBranch3MkVBalBranch255(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, eh) → new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, new_primMulNat1(zzz1147), eh)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Zero, eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Zero, eh)
new_mkVBalBranch3MkVBalBranch160(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, zzz1152, zzz1153, zzz1154, zzz1155, Succ(zzz12530), eh) → new_mkVBalBranch3MkVBalBranch169(zzz1145, zzz1146, zzz1147, zzz1148, zzz1149, zzz1150, zzz1151, Succ(zzz1152), zzz1153, zzz1154, zzz1155, Succ(Succ(zzz1152)), Succ(zzz12530), eh)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Succ(zzz5200), ef) → new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, zzz5190, zzz5200, ef)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Zero, Succ(zzz5200), ef) → new_mkBalBranch(zzz509, zzz510, new_mkVBalBranch4(zzz518, Branch(zzz514, zzz515, Neg(Succ(Zero)), zzz516, zzz517), zzz512, ef), zzz513, ty_Ordering, ef)
new_mkVBalBranch3MkVBalBranch253(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, Succ(zzz5190), Zero, ef) → new_mkVBalBranch3MkVBalBranch250(zzz509, zzz510, zzz511, zzz512, zzz513, zzz514, zzz515, zzz516, zzz517, zzz518, ef)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Zero, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), EQ, zzz41, Branch(zzz540, zzz541, Neg(Zero), zzz543, zzz544), Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), ty_Ordering, bb)
new_mkVBalBranch3MkVBalBranch150(zzz440, zzz441, zzz44200, zzz443, zzz444, zzz540, zzz541, zzz543, zzz544, zzz41, Succ(zzz1290), bb) → new_mkBalBranch(zzz540, zzz541, zzz543, new_mkVBalBranch4(zzz41, zzz544, Branch(zzz440, zzz441, Neg(Succ(zzz44200)), zzz443, zzz444), bb), ty_Ordering, bb)
new_splitGT40(bb) → new_emptyFM(bb)
new_splitLT14(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb)
new_splitLT26(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_intersectFM_C2Lts(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT9(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT9(zzz79, zzz80, zzz81, zzz82, db) → new_splitLT24(zzz79, zzz80, zzz81, zzz82, db)
new_splitLT13(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, zzz444, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT14(zzz441, zzz442, zzz443, zzz444, bb), bb)
new_splitLT12(Branch(LT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch2(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_splitLT12(Branch(GT, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_splitLT26(zzz19931, zzz19932, zzz19933, zzz19934, df)
new_splitLT12(Branch(EQ, zzz19931, zzz19932, zzz19933, zzz19934), df) → new_mkVBalBranch4(zzz19931, zzz19933, new_splitLT12(zzz19934, df), df)
new_splitLT12(EmptyFM, df) → new_splitLT40(df)
new_splitLT40(bb) → new_emptyFM(bb)
new_splitGT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb)
new_splitGT25(zzz41, zzz42, zzz43, zzz44, bb) → zzz44
new_intersectFM_C2Gts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca)
new_splitGT28(zzz902, zzz903, zzz904, zzz905, ca) → new_mkVBalBranch3(zzz902, new_splitGT19(zzz904, ca), zzz905, ca)
new_splitGT19(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT19(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT19(EmptyFM, be) → new_splitGT40(be)
new_splitGT19(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitGT211(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitGT211(zzz886, zzz887, zzz888, zzz889, be) → new_mkVBalBranch4(zzz886, new_splitGT19(zzz888, be), zzz889, be)
new_splitGT8(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT6(bb), zzz44, bb)
new_splitGT6(bb) → new_splitGT41(bb)
new_intersectFM_C2Lts2(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca)
new_splitLT25(zzz902, zzz903, zzz904, zzz905, ca) → new_splitLT16(zzz904, ca)
new_splitLT29(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT16(zzz888, be)
new_splitLT16(Branch(EQ, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT29(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT16(Branch(GT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT25(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT16(EmptyFM, be) → new_splitLT42(be)
new_splitLT16(Branch(LT, zzz8881, zzz8882, zzz8883, zzz8884), be) → new_splitLT28(zzz8881, zzz8882, zzz8883, zzz8884, be)
new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb) → zzz43
new_splitLT42(bb) → new_emptyFM(bb)
new_intersectFM_C2Lts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitLT29(zzz886, zzz887, zzz888, zzz889, be)
new_intersectFM_C2Lts0(zzz1993, df) → new_splitLT12(zzz1993, df)
new_splitLT10(zzz41, zzz42, zzz43, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT18(bb), bb)
new_splitLT18(bb) → new_splitLT40(bb)
new_splitGT5(zzz41, zzz42, zzz44, bb) → new_mkVBalBranch3(zzz41, new_splitGT16(bb), zzz44, bb)
new_intersectFM_C2Gts3(zzz917, zzz918, zzz919, zzz920, ce) → new_splitGT26(zzz917, zzz918, zzz919, zzz920, ce)
new_splitLT3(zzz41, zzz42, zzz43, zzz44, bb) → new_splitLT28(zzz41, zzz42, zzz43, zzz44, bb)
new_intersectFM_C2Gts1(zzz886, zzz887, zzz888, zzz889, be) → new_splitGT211(zzz886, zzz887, zzz888, zzz889, be)
new_splitLT11(zzz41, zzz42, zzz43, zzz441, zzz442, zzz443, bb) → new_mkVBalBranch2(zzz41, zzz43, new_splitLT10(zzz441, zzz442, zzz443, bb), bb)
new_splitLT6(bb) → new_splitLT41(bb)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_splitLT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch281(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT18(x0)
new_mkVBalBranch3MkVBalBranch275(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT14(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT19(Branch(LT, x0, x1, x2, x3), x4)
new_splitLT41(x0)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primMulNat0(x0)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_primMinusNat0(Zero, Zero)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_splitLT12(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_intersectFM_C2Lts(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch269(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_primPlusNat2(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Zero, x5, x6)
new_intersectFM_C2Gts1(x0, x1, x2, x3, x4)
new_splitGT8(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_splitGT16(x0)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch286(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch30(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch249(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_splitLT16(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch292(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitGT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Zero, Zero)
new_splitLT40(x0)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_addToFM1(x0, x1, x2)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5)
new_primPlusNat1(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch285(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_primPlusInt(x0, Neg(x1))
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_splitLT3(x0, x1, x2, x3, x4)
new_addToFM_C4(EmptyFM, x0, x1)
new_splitGT211(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch260(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Gts0(x0, x1)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT17(EmptyFM, x0)
new_splitLT6(x0)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_splitGT18(Branch(LT, x0, x1, x2, x3), x4)
new_splitGT19(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch290(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch284(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT4(x0, x1, x2, x3)
new_primMulNat(Zero)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
new_primPlusInt(x0, Pos(x1))
new_splitGT28(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch266(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch277(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_intersectFM_C2Lts2(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch2(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_splitLT7(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_addToFM_C2(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch259(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch246(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT24(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_intersectFM_C2Gts(x0, x1, x2, x3, x4)
new_primPlusInt0(Pos(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch251(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitLT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitLT9(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, Zero, x9)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C3(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Succ(Succ(x11)), x12)
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_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitLT23(x0, x1, x2, x3, x4)
new_splitGT15(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C2(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_primPlusNat2(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitGT27(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch289(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch256(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_addToFM_C3(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT29(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, Zero, x4, x5)
new_intersectFM_C2Lts3(x0, x1, x2, x3, x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_primMulNat1(x0)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch250(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch255(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_splitGT18(EmptyFM, x0)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_intersectFM_C2Gts3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_splitLT13(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_splitGT12(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, Zero, x11)
new_splitLT28(x0, x1, x2, x3, x4)
new_primPlusNat2(Succ(x0), Succ(x1))
new_mkVBalBranch3MkVBalBranch152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch274(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_splitLT16(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch272(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT17(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT14(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitLT16(EmptyFM, x0)
new_splitLT26(x0, x1, x2, x3, x4)
new_primPlusNat3(Succ(x0))
new_splitLT42(x0)
new_addToFM0(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat2(Succ(x0))
new_mkBalBranch6MkBalBranch41(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_splitLT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_intersectFM_C2Lts0(x0, x1)
new_addToFM2(x0, x1, x2)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_splitGT12(EmptyFM, x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_intersectFM_C2Lts1(x0, x1, x2, x3, x4)
new_addToFM_C3(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitGT13(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch264(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch276(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_addToFM_C3(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_primMinusNat0(Succ(x0), Zero)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT25(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch273(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, Zero, x11)
new_mkVBalBranch2(x0, EmptyFM, x1, x2)
new_splitGT19(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch247(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch282(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch268(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_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch253(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_primPlusNat3(Zero)
new_mkVBalBranch3MkVBalBranch254(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch248(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Succ(Zero), x10)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch2(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch278(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch288(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_intersectFM_C2Gts2(x0, x1, x2, x3, x4)
new_splitLT16(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch265(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitGT42(x0)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch263(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_splitLT10(x0, x1, x2, x3)
new_splitGT18(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
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, Succ(x10), x11)
new_splitGT41(x0)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch257(x0, x1, Pos(Succ(x2)), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch270(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Zero), x10)
new_mkVBalBranch3MkVBalBranch261(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primPlusNat1(x0, Zero)
new_splitGT210(x0, x1, x2, x3, x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_splitGT40(x0)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_addToFM_C2(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch283(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Neg(Succ(Succ(Zero))), x2, x3, x4, x5, Zero, x6, x7, x8, Succ(Zero), x9)
new_splitGT6(x0)
new_mkBalBranch6MkBalBranch30(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch258(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch4(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_emptyFM(x0)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch280(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_splitGT3(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch273(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_addToFM_C4(Branch(EQ, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch291(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT12(Branch(LT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch279(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(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_mkVBalBranch3MkVBalBranch252(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch2(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_splitGT5(x0, x1, x2, x3)
new_primPlusInt0(Neg(x0), x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT17(Branch(GT, x0, x1, x2, x3), x4)
new_primPlusInt1(x0, Neg(x1))
new_mkVBalBranch3MkVBalBranch153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_splitLT17(Branch(EQ, x0, x1, x2, x3), x4)
new_mkVBalBranch3(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_splitGT26(x0, x1, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Succ(Succ(x2)))), x3, x4, x5, x6, Zero, x7, x8, x9, Succ(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch271(x0, x1, Neg(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_addToFM(x0, x1, x2)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch4(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_splitGT24(x0, x1, x2, x3, x4)
new_primMulNat2(Zero)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitGT18(Branch(GT, x0, x1, x2, x3), x4)
new_splitGT7(x0, x1, x2, x3, x4)
new_splitLT12(Branch(GT, x0, x1, x2, x3), x4)
new_mkVBalBranch3MkVBalBranch262(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM_C4(Branch(LT, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch171(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, x10, x11)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch268(x0, x1, Neg(Zero), x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_primMulNat(Succ(x0))
new_splitLT27(x0, x1, x2, x3, x4)
new_mkVBalBranch4(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch287(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch267(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C2(Branch(GT, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch4(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_sizeFM(EmptyFM, x0, x1)
new_splitGT19(Branch(EQ, x0, x1, x2, x3), x4)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)

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: