YES 90.34400000000001 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
  ((minusFM :: FiniteMap Bool b  ->  FiniteMap Bool a  ->  FiniteMap Bool b) :: FiniteMap Bool b  ->  FiniteMap Bool a  ->  FiniteMap Bool 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 
  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C (\old new ->new) fm key elt

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

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

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

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

  minusFM :: Ord a => FiniteMap a c  ->  FiniteMap a b  ->  FiniteMap a c
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt _ left right) = 
glueVBal (minusFM lts left) (minusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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
\oldnew→new

is transformed to
addToFM0 old new = new



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR

mainModule FiniteMap
  ((minusFM :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a) :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap a b = EmptyFM  | Branch a b Int (FiniteMap a b) (FiniteMap a b) 
  instance (Eq a, Eq b) => Eq (FiniteMap a b) where 
  addToFM :: Ord b => FiniteMap b a  ->  b  ->  a  ->  FiniteMap b a
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

  minusFM :: Ord b => FiniteMap b a  ->  FiniteMap b c  ->  FiniteMap b a
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt _ left right) = 
glueVBal (minusFM lts left) (minusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((minusFM :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a) :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a)

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

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

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

  minusFM :: Ord c => FiniteMap c b  ->  FiniteMap c a  ->  FiniteMap c b
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt _ left right) = 
glueVBal (minusFM lts left) (minusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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

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

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

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

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

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

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

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



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

mainModule FiniteMap
  ((minusFM :: FiniteMap Bool b  ->  FiniteMap Bool a  ->  FiniteMap Bool b) :: FiniteMap Bool b  ->  FiniteMap Bool a  ->  FiniteMap Bool 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 
  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 vww fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwx 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 wuu EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuv fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vzw vzx EmptyFM) = (key,elt)
findMax (Branch key elt vzy vzz fm_r) = findMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt wy EmptyFM wz) = (key,elt)
findMin (Branch key elt xu fm_l xv) = findMin 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 (vyy,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (vyz,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,vzu) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,vzv) = 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 yx yy yz zu zv) (Branch zx zy zz vuu vuv) 
 | sIZE_RATIO * size_l < size_r = 
mkBalBranch zx zy (glueVBal (Branch yx yy yz zu zv) vuu) vuv
 | sIZE_RATIO * size_r < size_l = 
mkBalBranch yx yy zu (glueVBal zv (Branch zx zy zz vuu vuv))
 | otherwise = 
glueBal (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv) where 
size_l = sizeFM (Branch yx yy yz zu zv)
size_r = sizeFM (Branch zx zy zz vuu vuv)

  minusFM :: Ord a => FiniteMap a b  ->  FiniteMap a c  ->  FiniteMap a b
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt wuw left right) = 
glueVBal (minusFM lts left) (minusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

  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 vxy (Branch key_rl elt_rl vxz 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 vxw fm_ll (Branch key_lr elt_lr vxx 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 vyu vyv vyw 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 vwz vxu vxv 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 vyx 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 vwy 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 wu wv ww wx) = 
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 vw vx vy vz) = 
let 
smallest_right_key = fst (findMin fm_r)
in key < smallest_right_key
right_size = sizeFM fm_r
unbox :: Int  ->  Int
unbox x = x

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Cond Reductions:
The following Function with conditions
splitLT EmptyFM split_key = emptyFM
splitLT (Branch key elt xw 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 xw fm_l fm_r) split_key = splitLT3 (Branch key elt xw fm_l fm_r) split_key

splitLT0 key elt xw fm_l fm_r split_key True = fm_l

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

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

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

splitLT4 EmptyFM split_key = emptyFM
splitLT4 wvw wvx = splitLT3 wvw wvx

The following Function with conditions
splitGT EmptyFM split_key = emptyFM
splitGT (Branch key elt xx 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 xx fm_l fm_r) split_key = splitGT3 (Branch key elt xx fm_l fm_r) split_key

splitGT0 key elt xx fm_l fm_r split_key True = fm_r

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

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

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

splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwu wwv = splitGT3 wwu wwv

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

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

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

glueVBal4 fm1 EmptyFM = fm1
glueVBal4 wwz wxu = glueVBal3 wwz wxu

glueVBal5 EmptyFM fm2 = fm2
glueVBal5 wxw wxx = glueVBal4 wxw wxx

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

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 vux vuy vuz vvu vvv) (Branch vvx vvy vvz vwu vwv) = mkVBalBranch3 key elt (Branch vux vuy vuz vvu vvv) (Branch vvx vvy vvz vwu vwv)

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

mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wyv wyw wyx wyy = mkVBalBranch3 wyv wyw wyx wyy

mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wzu wzv wzw wzx = mkVBalBranch4 wzu wzv wzw wzx

The following Function with conditions
mkBalBranch1 fm_L fm_R (Branch vwz vxu vxv 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 vwz vxu vxv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)

mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = double_R fm_L fm_R

mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise

mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

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

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

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

mkBalBranch02 fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyu vyv vyw 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 vxy (Branch key_rl elt_rl vxz 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 vxw fm_ll (Branch key_lr elt_lr vxx 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 vyu vyv vyw 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 vwz vxu vxv 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 vyx 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 vwy 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 vxy (Branch key_rl elt_rl vxz 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 vxw fm_ll (Branch key_lr elt_lr vxx 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 vyu vyv vyw fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyu vyv vyw fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyu vyv vyw fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vwz vxu vxv 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 vyx 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 vwy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 key elt fm_lr fm_r)
size_l  = sizeFM fm_L
size_r  = sizeFM fm_R

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

glueBal3 fm1 EmptyFM = fm1
glueBal3 xuv xuw = glueBal2 xuv xuw

glueBal4 EmptyFM fm2 = fm2
glueBal4 xuy xuz = glueBal3 xuy xuz

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

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

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

addToFM_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_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 xvw xvx xvy xvz = addToFM_C3 xvw xvx xvy xvz

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

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

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

compare3 x y = compare2 x y (x == y)

The following Function with conditions
undefined 
 | False
 = undefined

is transformed to
undefined  = undefined1

undefined0 True = undefined

undefined1  = undefined0 False



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

mainModule FiniteMap
  ((minusFM :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a) :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
  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 xvw xvx xvy xvz = addToFM_C3 xvw xvx xvy xvz

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vww fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwx 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 wuu EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuv 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 vzw vzx EmptyFM) = (key,elt)
findMax (Branch key elt vzy vzz fm_r) = findMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt wy EmptyFM wz) = (key,elt)
findMin (Branch key elt xu fm_l xv) = findMin 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 (vyy,mid_elt1) = mid_elt1
mid_elt2 = mid_elt20 vv3
mid_elt20 (vyz,mid_elt2) = mid_elt2
mid_key1 = mid_key10 vv2
mid_key10 (mid_key1,vzu) = mid_key1
mid_key2 = mid_key20 vv3
mid_key20 (mid_key2,vzv) = mid_key2
vv2 = findMax fm1
vv3 = findMin fm2

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xuv xuw = glueBal2 xuv xuw

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xuy xuz = glueBal3 xuy xuz

  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 yx yy yz zu zv) (Branch zx zy zz vuu vuv) = glueVBal3 (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

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

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 wwz wxu = glueVBal3 wwz wxu

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 wxw wxx = glueVBal4 wxw wxx

  minusFM :: Ord a => FiniteMap a b  ->  FiniteMap a c  ->  FiniteMap a b
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt wuw left right) = 
glueVBal (minusFM lts left) (minusFM gts right) where 
gts = splitGT fm1 split_key
lts = splitLT fm1 split_key

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

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

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

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wyv wyw wyx wyy = mkVBalBranch3 wyv wyw wyx wyy

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wzu wzv wzw wzx = mkVBalBranch4 wzu wzv wzw wzx

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xx fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwu wwv = splitGT3 wwu wwv

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

  
splitLT0 key elt xw fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wvw wvx = splitLT3 wvw wvx

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Let/Where Reductions:
The bindings of the following Let/Where expression
mkBalBranch5 key elt fm_L fm_R (size_l + size_r < 2)
where 
double_L fm_l (Branch key_r elt_r vxy (Branch key_rl elt_rl vxz 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 vxw fm_ll (Branch key_lr elt_lr vxx 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 vyu vyv vyw fm_rl fm_rr) = mkBalBranch02 fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr)
mkBalBranch00 fm_L fm_R vyu vyv vyw fm_rl fm_rr True = double_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr True = single_L fm_L fm_R
mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr False = mkBalBranch00 fm_L fm_R vyu vyv vyw fm_rl fm_rr otherwise
mkBalBranch02 fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch01 fm_L fm_R vyu vyv vyw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)
mkBalBranch1 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)
mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = double_R fm_L fm_R
mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr True = single_R fm_L fm_R
mkBalBranch11 fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch10 fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise
mkBalBranch12 fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch11 fm_L fm_R vwz vxu vxv 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 vyx 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 vwy 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
mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Single_R xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise

mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R otherwise

mkBalBranch6Single_L xwu xwv xww xwx fm_l (Branch key_r elt_r vyx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xwu xwv fm_l fm_rl) fm_rr

mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr)

mkBalBranch6Single_R xwu xwv xww xwx (Branch key_l elt_l vwy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xwu xwv fm_lr fm_r)

mkBalBranch6Double_L xwu xwv xww xwx fm_l (Branch key_r elt_r vxy (Branch key_rl elt_rl vxz fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xwu xwv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xww

mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Single_L xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr otherwise

mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_l xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_r xwu xwv xww xwx)

mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_r xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_l xwu xwv xww xwx)

mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)

mkBalBranch6Size_l xwu xwv xww xwx = sizeFM xwx

mkBalBranch6Double_R xwu xwv xww xwx (Branch key_l elt_l vxw fm_ll (Branch key_lr elt_lr vxx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xwu xwv fm_lrr fm_r)

mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Double_L xwu xwv xww xwx fm_L fm_R

mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Double_R xwu xwv xww xwx fm_L fm_R

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

are unpacked to the following functions on top level
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch zx zy (glueVBal (Branch yx yy yz zu zv) vuu) vuv
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv (sIZE_RATIO * glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv < glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv)

glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xwy xwz xxu xxv xxw)

glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch yx yy zu (glueVBal zv (Branch zx zy zz vuu vuv))
glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv otherwise

glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xxx xxy xxz xyu xyv)

glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = glueBal (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

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

are unpacked to the following functions on top level
minusFMGts xyw xyx = splitGT xyw xyx

minusFMLts xyw xyx = splitLT xyw xyx

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 wu wv ww wx) = 
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 vw vx vy vz) = 
let 
smallest_right_key  = fst (findMin fm_r)
in key < smallest_right_key
right_size  = sizeFM fm_r
unbox x = x

are unpacked to the following functions on top level
mkBranchRight_ok0 xyy xyz xzu fm_r key EmptyFM = True
mkBranchRight_ok0 xyy xyz xzu fm_r key (Branch right_key vw vx vy vz) = key < mkBranchRight_ok0Smallest_right_key fm_r

mkBranchBalance_ok xyy xyz xzu = True

mkBranchLeft_ok xyy xyz xzu = mkBranchLeft_ok0 xyy xyz xzu xyy xyz xyy

mkBranchRight_size xyy xyz xzu = sizeFM xzu

mkBranchLeft_ok0 xyy xyz xzu fm_l key EmptyFM = True
mkBranchLeft_ok0 xyy xyz xzu fm_l key (Branch left_key wu wv ww wx) = mkBranchLeft_ok0Biggest_left_key fm_l < key

mkBranchLeft_size xyy xyz xzu = sizeFM xyy

mkBranchUnbox xyy xyz xzu x = x

mkBranchRight_ok xyy xyz xzu = mkBranchRight_ok0 xyy xyz xzu xzu xyz xzu

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 xzv xzw xzx xzy = Branch xzv xzw (mkBranchUnbox xzx xzv xzy (1 + mkBranchLeft_size xzx xzv xzy + mkBranchRight_size xzx xzv xzy)) xzx xzy

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 (vyy,mid_elt1) = mid_elt1
mid_elt2  = mid_elt20 vv3
mid_elt20 (vyz,mid_elt2) = mid_elt2
mid_key1  = mid_key10 vv2
mid_key10 (mid_key1,vzu) = mid_key1
mid_key2  = mid_key20 vv3
mid_key20 (mid_key2,vzv) = mid_key2
vv2  = findMax fm1
vv3  = findMin fm2

are unpacked to the following functions on top level
glueBal2Vv3 xzz yuu = findMin xzz

glueBal2Mid_key10 xzz yuu (mid_key1,vzu) = mid_key1

glueBal2Mid_elt2 xzz yuu = glueBal2Mid_elt20 xzz yuu (glueBal2Vv3 xzz yuu)

glueBal2Mid_key20 xzz yuu (mid_key2,vzv) = mid_key2

glueBal2Mid_elt1 xzz yuu = glueBal2Mid_elt10 xzz yuu (glueBal2Vv2 xzz yuu)

glueBal2Vv2 xzz yuu = findMax yuu

glueBal2GlueBal0 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 xzz yuu) (glueBal2Mid_elt1 xzz yuu) (deleteMax fm1) fm2

glueBal2GlueBal1 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 xzz yuu) (glueBal2Mid_elt2 xzz yuu) fm1 (deleteMin fm2)
glueBal2GlueBal1 xzz yuu fm1 fm2 False = glueBal2GlueBal0 xzz yuu fm1 fm2 otherwise

glueBal2Mid_key2 xzz yuu = glueBal2Mid_key20 xzz yuu (glueBal2Vv3 xzz yuu)

glueBal2Mid_elt10 xzz yuu (vyy,mid_elt1) = mid_elt1

glueBal2Mid_key1 xzz yuu = glueBal2Mid_key10 xzz yuu (glueBal2Vv2 xzz yuu)

glueBal2Mid_elt20 xzz yuu (vyz,mid_elt2) = mid_elt2

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

are unpacked to the following functions on top level
mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yuv yuw yux yuy yuz)

mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vux vuy vvu (mkVBalBranch key elt vvv (Branch vvx vvy vvz vwu vwv))
mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv otherwise

mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBranch 13 key elt (Branch vux vuy vuz vvu vvv) (Branch vvx vvy vvz vwu vwv)

mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yvu yvv yvw yvx yvy)

mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vvx vvy (mkVBalBranch key elt (Branch vux vuy vuz vvu vvv) vwu) vwv
mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv (sIZE_RATIO * mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy < mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy)

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 yvz = fst (findMin yvz)

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 ywu = fst (findMax ywu)



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

mainModule FiniteMap
  ((minusFM :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a) :: FiniteMap Bool a  ->  FiniteMap Bool b  ->  FiniteMap Bool a)

module FiniteMap where
  import qualified Maybe
import qualified Prelude
  data FiniteMap b a = EmptyFM  | Branch b a Int (FiniteMap b a) (FiniteMap b a) 
  instance (Eq a, Eq b) => Eq (FiniteMap b a) where 
  addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xvw xvx xvy xvz = addToFM_C3 xvw xvx xvy xvz

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt vww fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwx 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 wuu EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuv 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 vzw vzx EmptyFM) = (key,elt)
findMax (Branch key elt vzy vzz fm_r) = findMax fm_r

  findMin :: FiniteMap a b  ->  (a,b)
findMin (Branch key elt wy EmptyFM wz) = (key,elt)
findMin (Branch key elt xu fm_l xv) = findMin 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 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 xzz yuu) (glueBal2Mid_elt1 xzz yuu) (deleteMax fm1) fm2

  
glueBal2GlueBal1 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 xzz yuu) (glueBal2Mid_elt2 xzz yuu) fm1 (deleteMin fm2)
glueBal2GlueBal1 xzz yuu fm1 fm2 False = glueBal2GlueBal0 xzz yuu fm1 fm2 otherwise

  
glueBal2Mid_elt1 xzz yuu = glueBal2Mid_elt10 xzz yuu (glueBal2Vv2 xzz yuu)

  
glueBal2Mid_elt10 xzz yuu (vyy,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 xzz yuu = glueBal2Mid_elt20 xzz yuu (glueBal2Vv3 xzz yuu)

  
glueBal2Mid_elt20 xzz yuu (vyz,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 xzz yuu = glueBal2Mid_key10 xzz yuu (glueBal2Vv2 xzz yuu)

  
glueBal2Mid_key10 xzz yuu (mid_key1,vzu) = mid_key1

  
glueBal2Mid_key2 xzz yuu = glueBal2Mid_key20 xzz yuu (glueBal2Vv3 xzz yuu)

  
glueBal2Mid_key20 xzz yuu (mid_key2,vzv) = mid_key2

  
glueBal2Vv2 xzz yuu = findMax yuu

  
glueBal2Vv3 xzz yuu = findMin xzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xuv xuw = glueBal2 xuv xuw

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xuy xuz = glueBal3 xuy xuz

  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 yx yy yz zu zv) (Branch zx zy zz vuu vuv) = glueVBal3 (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

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

  
glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = glueBal (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

  
glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch yx yy zu (glueVBal zv (Branch zx zy zz vuu vuv))
glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv otherwise

  
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch zx zy (glueVBal (Branch yx yy yz zu zv) vuu) vuv
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv (sIZE_RATIO * glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv < glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv)

  
glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xwy xwz xxu xxv xxw)

  
glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xxx xxy xxz xyu xyv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 wwz wxu = glueVBal3 wwz wxu

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 wxw wxx = glueVBal4 wxw wxx

  minusFM :: Ord c => FiniteMap c b  ->  FiniteMap c a  ->  FiniteMap c b
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt wuw left right) = glueVBal (minusFM (minusFMLts fm1 split_key) left) (minusFM (minusFMGts fm1 split_key) right)

  
minusFMGts xyw xyx = splitGT xyw xyx

  
minusFMLts xyw xyx = splitLT xyw xyx

  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_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < 2)

  
mkBalBranch6Double_L xwu xwv xww xwx fm_l (Branch key_r elt_r vxy (Branch key_rl elt_rl vxz fm_rll fm_rlr) fm_rr) = mkBranch 5 key_rl elt_rl (mkBranch 6 xwu xwv fm_l fm_rll) (mkBranch 7 key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xwu xwv xww xwx (Branch key_l elt_l vxw fm_ll (Branch key_lr elt_lr vxx fm_lrl fm_lrr)) fm_r = mkBranch 10 key_lr elt_lr (mkBranch 11 key_l elt_l fm_ll fm_lrl) (mkBranch 12 xwu xwv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Double_L xwu xwv xww xwx fm_L fm_R

  
mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Single_L xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr (sizeFM fm_rl < 2 * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Double_R xwu xwv xww xwx fm_L fm_R

  
mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Single_R xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr (sizeFM fm_lr < 2 * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch 2 key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_l xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_r xwu xwv xww xwx)

  
mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch 1 key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_r xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_l xwu xwv xww xwx)

  
mkBalBranch6Single_L xwu xwv xww xwx fm_l (Branch key_r elt_r vyx fm_rl fm_rr) = mkBranch 3 key_r elt_r (mkBranch 4 xwu xwv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xwu xwv xww xwx (Branch key_l elt_l vwy fm_ll fm_lr) fm_r = mkBranch 8 key_l elt_l fm_ll (mkBranch 9 xwu xwv fm_lr fm_r)

  
mkBalBranch6Size_l xwu xwv xww xwx = sizeFM xwx

  
mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xww

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

  
mkBranchBalance_ok xyy xyz xzu = True

  
mkBranchLeft_ok xyy xyz xzu = mkBranchLeft_ok0 xyy xyz xzu xyy xyz xyy

  
mkBranchLeft_ok0 xyy xyz xzu fm_l key EmptyFM = True
mkBranchLeft_ok0 xyy xyz xzu fm_l key (Branch left_key wu wv ww wx) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key ywu = fst (findMax ywu)

  
mkBranchLeft_size xyy xyz xzu = sizeFM xyy

  
mkBranchResult xzv xzw xzx xzy = Branch xzv xzw (mkBranchUnbox xzx xzv xzy (1 + mkBranchLeft_size xzx xzv xzy + mkBranchRight_size xzx xzv xzy)) xzx xzy

  
mkBranchRight_ok xyy xyz xzu = mkBranchRight_ok0 xyy xyz xzu xzu xyz xzu

  
mkBranchRight_ok0 xyy xyz xzu fm_r key EmptyFM = True
mkBranchRight_ok0 xyy xyz xzu fm_r key (Branch right_key vw vx vy vz) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvz = fst (findMin yvz)

  
mkBranchRight_size xyy xyz xzu = sizeFM xzu

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox xyy xyz xzu x = x

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

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

  
mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBranch 13 key elt (Branch vux vuy vuz vvu vvv) (Branch vvx vvy vvz vwu vwv)

  
mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vux vuy vvu (mkVBalBranch key elt vvv (Branch vvx vvy vvz vwu vwv))
mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv otherwise

  
mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vvx vvy (mkVBalBranch key elt (Branch vux vuy vuz vvu vvv) vwu) vwv
mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv (sIZE_RATIO * mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy < mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy)

  
mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yuv yuw yux yuy yuz)

  
mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yvu yvv yvw yvx yvy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wyv wyw wyx wyy = mkVBalBranch3 wyv wyw wyx wyy

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wzu wzv wzw wzx = mkVBalBranch4 wzu wzv wzw wzx

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  
splitGT0 key elt xx fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwu wwv = splitGT3 wwu wwv

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

  
splitLT0 key elt xw fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wvw wvx = splitLT3 wvw wvx

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Num Reduction: All numbers are transformed to thier corresponding representation with Pos, Neg, Succ and Zero.

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

mainModule FiniteMap
  (minusFM :: FiniteMap Bool b  ->  FiniteMap Bool a  ->  FiniteMap Bool 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 
  addToFM :: Ord a => FiniteMap a b  ->  a  ->  b  ->  FiniteMap a b
addToFM fm key elt = addToFM_C addToFM0 fm key elt

  
addToFM0 old new = new

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

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

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

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

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

  
addToFM_C4 combiner EmptyFM key elt = unitFM key elt
addToFM_C4 xvw xvx xvy xvz = addToFM_C3 xvw xvx xvy xvz

  deleteMax :: Ord b => FiniteMap b a  ->  FiniteMap b a
deleteMax (Branch key elt vww fm_l EmptyFM) = fm_l
deleteMax (Branch key elt vwx 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 wuu EmptyFM fm_r) = fm_r
deleteMin (Branch key elt wuv fm_l fm_r) = mkBalBranch key elt (deleteMin fm_l) fm_r

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

  findMax :: FiniteMap b a  ->  (b,a)
findMax (Branch key elt vzw vzx EmptyFM) = (key,elt)
findMax (Branch key elt vzy vzz fm_r) = findMax fm_r

  findMin :: FiniteMap b a  ->  (b,a)
findMin (Branch key elt wy EmptyFM wz) = (key,elt)
findMin (Branch key elt xu fm_l xv) = findMin 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 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key1 xzz yuu) (glueBal2Mid_elt1 xzz yuu) (deleteMax fm1) fm2

  
glueBal2GlueBal1 xzz yuu fm1 fm2 True = mkBalBranch (glueBal2Mid_key2 xzz yuu) (glueBal2Mid_elt2 xzz yuu) fm1 (deleteMin fm2)
glueBal2GlueBal1 xzz yuu fm1 fm2 False = glueBal2GlueBal0 xzz yuu fm1 fm2 otherwise

  
glueBal2Mid_elt1 xzz yuu = glueBal2Mid_elt10 xzz yuu (glueBal2Vv2 xzz yuu)

  
glueBal2Mid_elt10 xzz yuu (vyy,mid_elt1) = mid_elt1

  
glueBal2Mid_elt2 xzz yuu = glueBal2Mid_elt20 xzz yuu (glueBal2Vv3 xzz yuu)

  
glueBal2Mid_elt20 xzz yuu (vyz,mid_elt2) = mid_elt2

  
glueBal2Mid_key1 xzz yuu = glueBal2Mid_key10 xzz yuu (glueBal2Vv2 xzz yuu)

  
glueBal2Mid_key10 xzz yuu (mid_key1,vzu) = mid_key1

  
glueBal2Mid_key2 xzz yuu = glueBal2Mid_key20 xzz yuu (glueBal2Vv3 xzz yuu)

  
glueBal2Mid_key20 xzz yuu (mid_key2,vzv) = mid_key2

  
glueBal2Vv2 xzz yuu = findMax yuu

  
glueBal2Vv3 xzz yuu = findMin xzz

  
glueBal3 fm1 EmptyFM = fm1
glueBal3 xuv xuw = glueBal2 xuv xuw

  
glueBal4 EmptyFM fm2 = fm2
glueBal4 xuy xuz = glueBal3 xuy xuz

  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 yx yy yz zu zv) (Branch zx zy zz vuu vuv) = glueVBal3 (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

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

  
glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = glueBal (Branch yx yy yz zu zv) (Branch zx zy zz vuu vuv)

  
glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch yx yy zu (glueVBal zv (Branch zx zy zz vuu vuv))
glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal0 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv otherwise

  
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv True = mkBalBranch zx zy (glueVBal (Branch yx yy yz zu zv) vuu) vuv
glueVBal3GlueVBal2 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv False = glueVBal3GlueVBal1 xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv yx yy yz zu zv zx zy zz vuu vuv (sIZE_RATIO * glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv < glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv)

  
glueVBal3Size_l xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xwy xwz xxu xxv xxw)

  
glueVBal3Size_r xwy xwz xxu xxv xxw xxx xxy xxz xyu xyv = sizeFM (Branch xxx xxy xxz xyu xyv)

  
glueVBal4 fm1 EmptyFM = fm1
glueVBal4 wwz wxu = glueVBal3 wwz wxu

  
glueVBal5 EmptyFM fm2 = fm2
glueVBal5 wxw wxx = glueVBal4 wxw wxx

  minusFM :: Ord a => FiniteMap a c  ->  FiniteMap a b  ->  FiniteMap a c
minusFM EmptyFM fm2 = emptyFM
minusFM fm1 EmptyFM = fm1
minusFM fm1 (Branch split_key elt wuw left right) = glueVBal (minusFM (minusFMLts fm1 split_key) left) (minusFM (minusFMGts fm1 split_key) right)

  
minusFMGts xyw xyx = splitGT xyw xyx

  
minusFMLts xyw xyx = splitLT xyw xyx

  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_R fm_L key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_R fm_L + mkBalBranch6Size_r key elt fm_R fm_L < Pos (Succ (Succ Zero)))

  
mkBalBranch6Double_L xwu xwv xww xwx fm_l (Branch key_r elt_r vxy (Branch key_rl elt_rl vxz 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))))))) xwu xwv fm_l fm_rll) (mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))) key_r elt_r fm_rlr fm_rr)

  
mkBalBranch6Double_R xwu xwv xww xwx (Branch key_l elt_l vxw fm_ll (Branch key_lr elt_lr vxx 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))))))))))))) xwu xwv fm_lrr fm_r)

  
mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr)

  
mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Double_L xwu xwv xww xwx fm_L fm_R

  
mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr True = mkBalBranch6Single_L xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr False = mkBalBranch6MkBalBranch00 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr otherwise

  
mkBalBranch6MkBalBranch02 xwu xwv xww xwx fm_L fm_R (Branch vyu vyv vyw fm_rl fm_rr) = mkBalBranch6MkBalBranch01 xwu xwv xww xwx fm_L fm_R vyu vyv vyw fm_rl fm_rr (sizeFM fm_rl < Pos (Succ (Succ Zero)) * sizeFM fm_rr)

  
mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr)

  
mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Double_R xwu xwv xww xwx fm_L fm_R

  
mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr True = mkBalBranch6Single_R xwu xwv xww xwx fm_L fm_R
mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr False = mkBalBranch6MkBalBranch10 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr otherwise

  
mkBalBranch6MkBalBranch12 xwu xwv xww xwx fm_L fm_R (Branch vwz vxu vxv fm_ll fm_lr) = mkBalBranch6MkBalBranch11 xwu xwv xww xwx fm_L fm_R vwz vxu vxv fm_ll fm_lr (sizeFM fm_lr < Pos (Succ (Succ Zero)) * sizeFM fm_ll)

  
mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch (Pos (Succ (Succ Zero))) key elt fm_L fm_R

  
mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch1 xwu xwv xww xwx fm_L fm_R fm_L
mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch2 xwu xwv xww xwx key elt fm_L fm_R otherwise

  
mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R True = mkBalBranch6MkBalBranch0 xwu xwv xww xwx fm_L fm_R fm_R
mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch3 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_l xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_r xwu xwv xww xwx)

  
mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R True = mkBranch (Pos (Succ Zero)) key elt fm_L fm_R
mkBalBranch6MkBalBranch5 xwu xwv xww xwx key elt fm_L fm_R False = mkBalBranch6MkBalBranch4 xwu xwv xww xwx key elt fm_L fm_R (mkBalBranch6Size_r xwu xwv xww xwx > sIZE_RATIO * mkBalBranch6Size_l xwu xwv xww xwx)

  
mkBalBranch6Single_L xwu xwv xww xwx fm_l (Branch key_r elt_r vyx fm_rl fm_rr) = mkBranch (Pos (Succ (Succ (Succ Zero)))) key_r elt_r (mkBranch (Pos (Succ (Succ (Succ (Succ Zero))))) xwu xwv fm_l fm_rl) fm_rr

  
mkBalBranch6Single_R xwu xwv xww xwx (Branch key_l elt_l vwy 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)))))))))) xwu xwv fm_lr fm_r)

  
mkBalBranch6Size_l xwu xwv xww xwx = sizeFM xwx

  
mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xww

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

  
mkBranchBalance_ok xyy xyz xzu = True

  
mkBranchLeft_ok xyy xyz xzu = mkBranchLeft_ok0 xyy xyz xzu xyy xyz xyy

  
mkBranchLeft_ok0 xyy xyz xzu fm_l key EmptyFM = True
mkBranchLeft_ok0 xyy xyz xzu fm_l key (Branch left_key wu wv ww wx) = mkBranchLeft_ok0Biggest_left_key fm_l < key

  
mkBranchLeft_ok0Biggest_left_key ywu = fst (findMax ywu)

  
mkBranchLeft_size xyy xyz xzu = sizeFM xyy

  
mkBranchResult xzv xzw xzx xzy = Branch xzv xzw (mkBranchUnbox xzx xzv xzy (Pos (Succ Zero) + mkBranchLeft_size xzx xzv xzy + mkBranchRight_size xzx xzv xzy)) xzx xzy

  
mkBranchRight_ok xyy xyz xzu = mkBranchRight_ok0 xyy xyz xzu xzu xyz xzu

  
mkBranchRight_ok0 xyy xyz xzu fm_r key EmptyFM = True
mkBranchRight_ok0 xyy xyz xzu fm_r key (Branch right_key vw vx vy vz) = key < mkBranchRight_ok0Smallest_right_key fm_r

  
mkBranchRight_ok0Smallest_right_key yvz = fst (findMin yvz)

  
mkBranchRight_size xyy xyz xzu = sizeFM xzu

  mkBranchUnbox :: Ord a =>  ->  (FiniteMap a b) ( ->  a ( ->  (FiniteMap a b) (Int  ->  Int)))
mkBranchUnbox xyy xyz xzu x = x

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

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

  
mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBranch (Pos (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ (Succ Zero)))))))))))))) key elt (Branch vux vuy vuz vvu vvv) (Branch vvx vvy vvz vwu vwv)

  
mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vux vuy vvu (mkVBalBranch key elt vvv (Branch vvx vvy vvz vwu vwv))
mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch0 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv otherwise

  
mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv True = mkBalBranch vvx vvy (mkVBalBranch key elt (Branch vux vuy vuz vvu vvv) vwu) vwv
mkVBalBranch3MkVBalBranch2 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv False = mkVBalBranch3MkVBalBranch1 yuv yuw yux yuy yuz yvu yvv yvw yvx yvy key elt vux vuy vuz vvu vvv vvx vvy vvz vwu vwv (sIZE_RATIO * mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy < mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy)

  
mkVBalBranch3Size_l yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yuv yuw yux yuy yuz)

  
mkVBalBranch3Size_r yuv yuw yux yuy yuz yvu yvv yvw yvx yvy = sizeFM (Branch yvu yvv yvw yvx yvy)

  
mkVBalBranch4 key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch4 wyv wyw wyx wyy = mkVBalBranch3 wyv wyw wyx wyy

  
mkVBalBranch5 key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch5 wzu wzv wzw wzx = mkVBalBranch4 wzu wzv wzw wzx

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

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

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

  
splitGT0 key elt xx fm_l fm_r split_key True = fm_r

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

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

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

  
splitGT4 EmptyFM split_key = emptyFM
splitGT4 wwu wwv = splitGT3 wwu wwv

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

  
splitLT0 key elt xw fm_l fm_r split_key True = fm_l

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

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

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

  
splitLT4 EmptyFM split_key = emptyFM
splitLT4 wvw wvx = splitLT3 wvw wvx

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


Haskell To QDPs


↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ 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

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

new_glueBal2Mid_elt10(ywv801, ywv802, ywv803, ywv804, ywv805, ywv806, ywv807, ywv808, ywv809, ywv810, ywv811, ywv812, ywv813, ywv814, Branch(ywv8150, ywv8151, ywv8152, ywv8153, ywv8154), h, ba) → new_glueBal2Mid_elt10(ywv801, ywv802, ywv803, ywv804, ywv805, ywv806, ywv807, ywv808, ywv809, ywv810, ywv8150, ywv8151, ywv8152, ywv8153, ywv8154, 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
          ↳ 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

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

new_glueBal2Mid_key10(ywv783, ywv784, ywv785, ywv786, ywv787, ywv788, ywv789, ywv790, ywv791, ywv792, ywv793, ywv794, ywv795, ywv796, Branch(ywv7970, ywv7971, ywv7972, ywv7973, ywv7974), h, ba) → new_glueBal2Mid_key10(ywv783, ywv784, ywv785, ywv786, ywv787, ywv788, ywv789, ywv790, ywv791, ywv792, ywv7970, ywv7971, ywv7972, ywv7973, ywv7974, 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
          ↳ 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

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

new_glueBal2Mid_elt20(ywv767, ywv768, ywv769, ywv770, ywv771, ywv772, ywv773, ywv774, ywv775, ywv776, ywv777, ywv778, ywv779, Branch(ywv7800, ywv7801, ywv7802, ywv7803, ywv7804), ywv781, h, ba) → new_glueBal2Mid_elt20(ywv767, ywv768, ywv769, ywv770, ywv771, ywv772, ywv773, ywv774, ywv775, ywv776, ywv7800, ywv7801, ywv7802, ywv7803, ywv7804, 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
          ↳ 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

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

new_glueBal2Mid_key20(ywv751, ywv752, ywv753, ywv754, ywv755, ywv756, ywv757, ywv758, ywv759, ywv760, ywv761, ywv762, ywv763, Branch(ywv7640, ywv7641, ywv7642, ywv7643, ywv7644), ywv765, h, ba) → new_glueBal2Mid_key20(ywv751, ywv752, ywv753, ywv754, ywv755, ywv756, ywv757, ywv758, ywv759, ywv760, ywv7640, ywv7641, ywv7642, ywv7643, ywv7644, 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
          ↳ 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

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

new_primPlusNat(Succ(ywv62000)) → new_primPlusNat(ywv62000)

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
          ↳ 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

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

new_primMinusNat(Succ(ywv41900), Succ(ywv39800)) → new_primMinusNat(ywv41900, ywv39800)

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
          ↳ 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

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

new_primPlusNat0(Succ(ywv310), Succ(ywv3200)) → new_primPlusNat0(ywv310, ywv3200)

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
          ↳ 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

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

new_mkBalBranch6MkBalBranch11(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv1033000), Succ(ywv104500), h, ba) → new_mkBalBranch6MkBalBranch11(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv1033000, ywv104500, 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
          ↳ 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

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

new_mkBalBranch6MkBalBranch3(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv909000), Succ(ywv98000), h, ba) → new_mkBalBranch6MkBalBranch3(ywv40930, ywv40931, ywv40934, ywv714, ywv909000, ywv98000, 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
          ↳ 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

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

new_mkBalBranch6MkBalBranch01(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv912000), Succ(ywv101100), h, ba) → new_mkBalBranch6MkBalBranch01(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv912000, ywv101100, 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
          ↳ 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

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

new_mkBalBranch6MkBalBranch4(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv798000), Succ(ywv86700), h, ba) → new_mkBalBranch6MkBalBranch4(ywv40930, ywv40931, ywv40934, ywv714, ywv798000, ywv86700, 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
          ↳ 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

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

new_deleteMax(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), h, ba) → new_deleteMax(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, 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
          ↳ 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

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

new_deleteMin(ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, h, ba) → new_deleteMin(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, 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
          ↳ 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

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

new_glueBal2GlueBal1(ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, Succ(ywv681000), Succ(ywv680000), h, ba) → new_glueBal2GlueBal1(ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv681000, ywv680000, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6690, h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv65900, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, Zero, h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65900, ywv6690, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Succ(Succ(ywv620000)), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65900), ywv6690, h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65900, ywv6690, h, ba)
new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal16(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65900, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Neg(ywv6200), h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6530, h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv62000, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal16(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(Succ(ywv659000)), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, Succ(ywv6530), Pos(ywv6200), h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Succ(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv66800)), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv62000), ywv6530, h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, ywv6530, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Pos(ywv6590), h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv659, h, ba) → new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv659, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, ywv6530, h, ba)
new_glueVBal3GlueVBal16(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv66800), Succ(Succ(ywv659000)), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(Succ(ywv620000)), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv66800), Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv620, h, ba) → new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv620, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv6520, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primPlusNat1(Zero) → Zero
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv40930, ywv40931, ywv40932, ywv40933, ywv40934), h, ba)
new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054), h, ba)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bb, bc) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

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

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

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

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

new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6690, h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv65900, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Neg(ywv6200), h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6530, h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv62000, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, Succ(ywv6530), Pos(ywv6200), h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv66800)), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65900, ywv6690, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Pos(ywv6590), h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, ywv6530, h, ba)
new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv659, h, ba) → new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv659, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv66800), Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv620, h, ba) → new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv620, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv6520, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primPlusNat1(Zero) → Zero
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv40930, ywv40931, ywv40932, ywv40933, ywv40934), h, ba)
new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054), h, ba)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bb, bc) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

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

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

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

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

new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6690, h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Succ(ywv620000))), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv65200), Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65200, ywv620000, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal15(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv65900, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv65200)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Zero), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Neg(ywv6200), h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)
new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv6530, h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal26(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, ywv62000, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, Branch(ywv409330, ywv409331, ywv409332, ywv409333, ywv409334), ywv40934, Succ(ywv6530), Pos(ywv6200), h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Neg(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(Succ(ywv66800)), Pos(Succ(Succ(ywv659000))), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Neg(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv65900, ywv6690, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, Branch(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544), ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6690), Pos(ywv6590), h, ba) → new_glueVBal3(ywv40540, ywv40541, ywv40542, ywv40543, ywv40544, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal21(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6530), Neg(Succ(ywv62000)), h, ba) → new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv62000, ywv6530, h, ba)
new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv659, h, ba) → new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv659, h, ba)
new_glueVBal3GlueVBal22(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Succ(ywv620000), h, ba) → new_glueVBal3GlueVBal24(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv6520), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Succ(ywv66800), Succ(ywv659000), h, ba) → new_glueVBal3GlueVBal13(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv66800, ywv659000, h, ba)
new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv620, h, ba) → new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), ywv620, h, ba)
new_glueVBal3GlueVBal12(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Succ(ywv65900)), h, ba) → new_glueVBal3GlueVBal14(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal2(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6270), ywv620, h, ba) → new_glueVBal3GlueVBal20(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6270), ywv620, h, ba)
new_glueVBal3(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba) → new_glueVBal3GlueVBal29(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv409330, ywv409331, ywv409332, ywv409333, ywv409334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, ywv6520, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba)
new_glueVBal3GlueVBal10(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, Pos(ywv6650), ywv659, h, ba) → new_glueVBal3GlueVBal11(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_primMulNat(ywv6650), ywv659, h, ba)
new_glueVBal3GlueVBal23(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_glueVBal3GlueVBal1(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba), h, ba)

The TRS R consists of the following rules:

new_glueVBal3Size_l(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054), h, ba)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bb, bc) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_glueVBal3Size_r(ywv4050, ywv4051, ywv4052, ywv4053, ywv4054, ywv40930, ywv40931, ywv40932, ywv40933, ywv40934, h, ba) → new_sizeFM(Branch(ywv40930, ywv40931, ywv40932, ywv40933, ywv40934), h, ba)

The set Q consists of the following terms:

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

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

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



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

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

new_addToFM_C(Branch(True, ywv251, ywv252, ywv253, ywv254), ywv31, h) → new_addToFM_C(ywv253, ywv31, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv623000), Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv10690, bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv9900, ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch119(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Pos(Succ(Succ(ywv706000))), h) → new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, h)
new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv104400)), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch115(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Succ(Succ(ywv1035000)), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Pos(Succ(Succ(ywv716000))), h) → new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, h)
new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, h)
new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Zero, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Succ(ywv664000))), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv747000), Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv62400)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(Succ(ywv104400)), ba) → new_mkVBalBranch3MkVBalBranch115(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv104400, Zero, ba)
new_mkVBalBranch3MkVBalBranch122(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5730), h) → new_mkVBalBranch3MkVBalBranch144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9900), ba) → new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv103600)), ba) → new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv103600, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv24200, ywv1280, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2620), h) → new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv8440), ba) → new_mkVBalBranch(ywv842, ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836, ywv840, ba)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10680), bb) → new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Succ(ywv10660), bb) → new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10650, ywv10660, bb)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch140(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(Succ(ywv1070000)), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch1(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5740), h) → new_mkVBalBranch3MkVBalBranch148(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch147(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch148(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57400), Neg(Succ(Succ(ywv718000))), h) → new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, h)
new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv67400)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71700)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch140(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Succ(Succ(ywv1070000)), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv664000), Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Pos(ywv10370), ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch0(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv103700), ywv9900, ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv103700, ywv9900, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10690), bb) → new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv107200), ywv10690, bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107200, ywv10690, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2650), h) → new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv74800)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Succ(ywv107200)), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107200, ywv10690, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5700), h) → new_mkVBalBranch3MkVBalBranch119(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Pos(ywv7470), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Succ(ywv8440), ba) → new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv8430, ywv8440, ba)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv24200), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Pos(ywv6230), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv10660), bb) → new_mkVBalBranch(ywv1064, ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058, ywv1062, bb)
new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Succ(ywv747000))), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(Succ(ywv107300)), bb) → new_mkVBalBranch3MkVBalBranch140(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107300, Zero, bb)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9790), ba) → new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch148(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57400), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch122(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv6210), h) → new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Pos(ywv10720), bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107300)), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch148(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, Pos(ywv7180), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57200)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch148(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107100)), bb) → new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv107100, bb)
new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv66300)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Pos(Succ(Succ(ywv716000))), h) → new_mkVBalBranch3MkVBalBranch147(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv24200), Zero, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch119(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Pos(Succ(Succ(ywv706000))), h) → new_mkVBalBranch3MkVBalBranch122(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Succ(ywv623000))), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(ywv2420), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71900)), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Succ(ywv103700)), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv103700, ywv9900, ba)
new_mkVBalBranch3MkVBalBranch115(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(Succ(ywv1035000)), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Pos(ywv6640), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv1260, ywv24200, h)
new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57600)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Zero, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch2(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch147(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57100)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bd, be) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 4 SCCs with 26 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv623000), Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv10690, bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv9900, ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv104400)), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Zero, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Succ(ywv664000))), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv747000), Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv62400)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9900), ba) → new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv103600)), ba) → new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv103600, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv24200, ywv1280, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2620), h) → new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv8440), ba) → new_mkVBalBranch(ywv842, ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836, ywv840, ba)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10680), bb) → new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Succ(ywv10660), bb) → new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10650, ywv10660, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch1(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv67400)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71700)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv664000), Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Pos(ywv10370), ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch0(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10690), bb) → new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2650), h) → new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv74800)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Succ(ywv107200)), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107200, ywv10690, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Pos(ywv7470), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Succ(ywv8440), ba) → new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv8430, ywv8440, ba)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Pos(ywv6230), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv24200), h)
new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv10660), bb) → new_mkVBalBranch(ywv1064, ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058, ywv1062, bb)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Succ(ywv747000))), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9790), ba) → new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv6210), h) → new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Pos(ywv10720), bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107300)), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57200)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107100)), bb) → new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv107100, bb)
new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv66300)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv24200), Zero, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Succ(ywv623000))), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(ywv2420), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71900)), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Succ(ywv103700)), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv103700, ywv9900, ba)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Pos(ywv6640), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57600)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv1260, ywv24200, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Zero, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch2(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57100)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bd, be) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv623000), Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv10690, bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv9900, ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv104400)), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Zero, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Succ(ywv664000))), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv747000), Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv62400)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch23(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9900), ba) → new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch22(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv103600)), ba) → new_mkVBalBranch3MkVBalBranch116(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv103600, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv24200, ywv1280, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2620), h) → new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv8440), ba) → new_mkVBalBranch(ywv842, ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836, ywv840, ba)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10680), bb) → new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Succ(ywv10660), bb) → new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10650, ywv10660, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch1(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch118(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch153(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv67400)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch110(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71700)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv664000), Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch154(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkVBalBranch3MkVBalBranch28(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb) → new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb), bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(ywv9110), ba) → new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), ba)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Pos(ywv10370), ba) → new_mkVBalBranch3(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ba)
new_mkVBalBranch0(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch24(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10690), bb) → new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ba) → new_mkVBalBranch3MkVBalBranch112(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2650), h) → new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch132(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch124(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv74800)), h) → new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Succ(ywv107200)), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107200, ywv10690, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Pos(ywv7470), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Succ(ywv8440), ba) → new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv8430, ywv8440, ba)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Pos(ywv6230), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv24200), h)
new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch26(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv10660), bb) → new_mkVBalBranch(ywv1064, ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058, ywv1062, bb)
new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv62100), Neg(Succ(Succ(ywv747000))), h) → new_mkVBalBranch3MkVBalBranch125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv1070000), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch13(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch131(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch134(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, bb) → new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, bb), bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch19(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9790), ba) → new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch133(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(ywv10670), bb) → new_mkVBalBranch3MkVBalBranch135(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), bb)
new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch15(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv6210), h) → new_mkVBalBranch3MkVBalBranch123(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch130(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch142(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Pos(ywv10720), bb) → new_mkVBalBranch1(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, bb)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch143(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107300)), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch17(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, ba)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57500)), h) → new_mkVBalBranch0(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57200)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch137(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107100)), bb) → new_mkVBalBranch3MkVBalBranch141(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv107100, bb)
new_mkVBalBranch3MkVBalBranch16(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv66300)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch138(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, bb)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch26(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv24200), Zero, h)
new_mkVBalBranch3MkVBalBranch111(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Pos(Succ(Succ(ywv1035000))), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch11(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26500), Neg(Succ(Zero)), h) → new_mkVBalBranch3MkVBalBranch155(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch10(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch128(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch127(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv26200), Neg(Succ(Succ(ywv623000))), h) → new_mkVBalBranch3MkVBalBranch129(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch25(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(ywv2420), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h)
new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv1035000), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch3MkVBalBranch149(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71900)), h) → new_mkVBalBranch3MkVBalBranch151(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Succ(ywv103700)), ba) → new_mkVBalBranch3MkVBalBranch113(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv103700, ywv9900, ba)
new_mkVBalBranch3MkVBalBranch152(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Pos(ywv6640), h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch14(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57600)), h) → new_mkVBalBranch2(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch2(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch21(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv1260, ywv24200, h)
new_mkVBalBranch3MkVBalBranch21(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Zero, ba) → new_mkVBalBranch3MkVBalBranch18(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ba), ba)
new_mkVBalBranch3MkVBalBranch136(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Pos(Succ(Succ(ywv1070000))), bb) → new_mkVBalBranch3MkVBalBranch139(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, bb)
new_mkVBalBranch3MkVBalBranch117(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch114(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ba)
new_mkVBalBranch2(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch27(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch1(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1(ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57100)), h) → new_mkVBalBranch3(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkVBalBranch(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), h) → new_mkVBalBranch3MkVBalBranch12(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch20(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bd, be) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, h)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ 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_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch150(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bd, be) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ 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_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, h)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ 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_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch146(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, bf) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, bf)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bc) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bc)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bd, be) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bd, be) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, h)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat3(Succ(x0), Succ(x1))
new_primMulNat(Succ(x0))
new_primMulNat1(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



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

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

new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch121(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_splitLT3(False, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, h)
new_splitLT3(False, ywv31, ywv32, EmptyFM, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, h)
new_splitLT3(True, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, False, h) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, False, 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 2 SCCs.

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

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

new_splitLT3(True, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, False, h) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, False, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_splitLT3(False, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, h)
new_splitLT3(False, ywv31, ywv32, EmptyFM, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C0(Branch(False, ywv341, ywv342, ywv343, ywv344), ywv31, h) → new_addToFM_C0(ywv344, ywv31, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch174(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(Succ(ywv1017000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch174(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(Succ(ywv1017000)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch174(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv102000, Zero, bb)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv101500), ywv9920, ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(Succ(ywv1013000)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(Succ(ywv1013000)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101600, Zero, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv101900), ywv9940, bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bc, bd) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 1 SCC with 10 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(EmptyFM, bc, bd) → Pos(Zero)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Neg(Succ(ywv968)), bb)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), bb) → new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch170(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Pos(Succ(Succ(ywv1017000))), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h) at position [10] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primMulNat1(x0)

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

new_primMulNat1(x0)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), Succ(ywv20200)), Succ(ywv20200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv968)), bb)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), bb) → new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch168(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch171(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch175(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch213(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch212(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200))), Succ(ywv20200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch217(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [10,0] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv968)), bb)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, bb) → new_mkVBalBranch3MkVBalBranch177(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [10] we obtained the following new rules:

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, bb) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, bb), bb) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ba), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, be) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, be)

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primMulNat0(x0)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat1(Succ(x0))
new_primMulNat(Zero)
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(x0), Succ(x1))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primMulNat(Succ(x0))
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)

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

new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, ba), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)



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

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

new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Succ(ywv101500)), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch180(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(Zero), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch159(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), ba) → new_mkVBalBranch3MkVBalBranch179(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, ba), ba) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bc, bd) → ywv2952
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

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

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



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch181(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), bb) → new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), bb) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv101900)), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, bb) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), ba) → new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat(Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Zero) → Zero
new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primMulNat(Succ(z7)), z11) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

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

new_primMulNat(Zero)
new_primMulNat(Succ(x0))



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primMulNat0(z7), Succ(z7)), z11) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

new_primMulNat0(x0)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), Succ(z7)), Succ(z7)), z11) at position [11,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, new_primPlusNat3(Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7))), Succ(z7)), z11) at position [11] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)



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

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

new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), ba) → new_mkVBalBranch3MkVBalBranch178(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, ba)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ba) → new_mkVBalBranch3MkVBalBranch161(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch158(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), ba) → new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(Succ(ywv954)), ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
By instantiating [15] the rule new_mkVBalBranch3MkVBalBranch160(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Pos(Succ(Succ(ywv1013000))), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba) we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(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_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x2 + x3 + x4 + x5   
POL(Neg(x1)) = x1   
POL(Pos(x1)) = x1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch3MkVBalBranch156(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch157(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch158(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch160(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch162(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch163(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5   
POL(new_mkVBalBranch3MkVBalBranch165(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x2 + x4   
POL(new_mkVBalBranch3MkVBalBranch166(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x2 + x4   
POL(new_mkVBalBranch3MkVBalBranch167(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch169(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch172(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch173(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5   
POL(new_mkVBalBranch3MkVBalBranch176(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch210(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch214(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x2 + x4 + x5   
POL(new_mkVBalBranch3MkVBalBranch29(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x2 + x4 + x5   
POL(new_mkVBalBranch4(x1, x2, x3, x4)) = x2   
POL(new_primPlusNat1(x1)) = 0   
POL(new_primPlusNat2(x1, x2)) = 0   
POL(new_primPlusNat3(x1, x2)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch165(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch166(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(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 2 less nodes.

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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h)

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

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

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

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



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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ DependencyGraphProof
                                                              ↳ 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
                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ UsableRulesProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                              ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h)

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

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

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

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



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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ DependencyGraphProof
                                                              ↳ 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
                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ UsableRulesProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                              ↳ QDPOrderProof
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(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_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, ba) → new_mkVBalBranch3MkVBalBranch157(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv959)), ba)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv34200), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch3MkVBalBranch156(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch157(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch158(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x5   
POL(new_mkVBalBranch3MkVBalBranch160(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch162(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x3 + x5   
POL(new_mkVBalBranch3MkVBalBranch163(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5   
POL(new_mkVBalBranch3MkVBalBranch167(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch169(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch172(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch173(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5   
POL(new_mkVBalBranch3MkVBalBranch176(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch210(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch211(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)) = x5   
POL(new_mkVBalBranch3MkVBalBranch214(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x5   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch29(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch4(x1, x2, x3, x4)) = x2   
POL(new_primPlusNat1(x1)) = 1 + x1   
POL(new_primPlusNat2(x1, x2)) = 1 + x1   
POL(new_primPlusNat3(x1, x2)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch160(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, Succ(z11), Pos(Succ(Succ(x12))), z12) → new_mkVBalBranch3MkVBalBranch162(z0, z1, Succ(x12), z3, z4, z5, z6, z7, z8, z9, z10, z11, x12, z12)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch157(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Pos(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch214(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch158(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(y_3)), z11) → new_mkVBalBranch3MkVBalBranch160(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(y_3), Pos(Succ(z2)), z11)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba) → new_mkVBalBranch4(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ba)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch156(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ba)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch211(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkVBalBranch4(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(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 8 less nodes.

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

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

new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch29(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch210(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), ba) → new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, ba)
new_mkVBalBranch3MkVBalBranch210(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), ba) → new_mkVBalBranch4(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

new_primPlusNat2(x0, Zero)
new_primPlusNat3(Succ(x0), Zero)
new_primPlusNat1(Zero)
new_primPlusNat1(Succ(x0))
new_primPlusNat2(x0, Succ(x1))
new_primPlusNat3(Zero, Succ(x0))
new_primPlusNat3(Zero, Zero)
new_primPlusNat3(Succ(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_mkVBalBranch3MkVBalBranch167(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Neg(Succ(z7)), z11) → new_mkVBalBranch3MkVBalBranch169(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(z7), z7)), z7)), z7))), z11)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x2 + x5   
POL(Neg(x1)) = 0   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch3MkVBalBranch167(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch169(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch172(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch173(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = x5   
POL(new_mkVBalBranch3MkVBalBranch176(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x5   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)) = 1 + x1 + x2 + x5   
POL(new_mkVBalBranch4(x1, x2, x3, x4)) = x2   
POL(new_primPlusNat1(x1)) = 0   
POL(new_primPlusNat2(x1, x2)) = 1   
POL(new_primPlusNat3(x1, x2)) = 0   

The following usable rules [17] were oriented: none



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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch176(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z11, Neg(Succ(z2)), z12) → new_mkVBalBranch3MkVBalBranch172(z0, z1, z2, z3, z4, z5, z6, z7, z8, z9, z10, z2, z11, z12)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch169(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), bb) → new_mkVBalBranch3MkVBalBranch176(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(Succ(ywv968)), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch218(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch3MkVBalBranch173(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, bb) → new_mkVBalBranch4(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), bb)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, bb) → new_mkVBalBranch3MkVBalBranch167(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv973)), bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 2 SCCs with 7 less nodes.

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

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

new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch216(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), bb) → new_mkVBalBranch4(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, bb)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)
new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), bb) → new_mkVBalBranch3MkVBalBranch216(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, bb)
new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, Succ(Succ(new_primPlusNat3(Succ(new_primPlusNat3(Succ(new_primPlusNat2(new_primPlusNat1(ywv20200), ywv20200)), ywv20200)), ywv20200))), h)
new_mkVBalBranch3MkVBalBranch215(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch4(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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



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

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

new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, bb)

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

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

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

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



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

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

new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), bb) → new_mkVBalBranch3MkVBalBranch172(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ Rewriting
                                          ↳ QDP
                                            ↳ Rewriting
                                              ↳ QDP
                                                ↳ Rewriting
                                                  ↳ QDP
                                                    ↳ Rewriting
                                                      ↳ QDP
                                                        ↳ Rewriting
                                                          ↳ QDP
                                                            ↳ DependencyGraphProof
                                                              ↳ 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
                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                      ↳ QDP
                                                                                                                                        ↳ Rewriting
                                                                                                                                          ↳ QDP
                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                              ↳ QDP
                                                                                                                                                ↳ Rewriting
                                                                                                                                                  ↳ QDP
                                                                                                                                                    ↳ Rewriting
                                                                                                                                                      ↳ QDP
                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                          ↳ QDP
                                                                                                                                                            ↳ Rewriting
                                                                                                                                                              ↳ QDP
                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                  ↳ QDP
                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                      ↳ QDP
                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                          ↳ QDP
                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                ↳ DependencyGraphProof
                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                    ↳ Instantiation
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ Rewriting
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                            ↳ Instantiation
                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                ↳ UsableRulesProof
                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                    ↳ Rewriting
                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                    ↳ UsableRulesProof
                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                        ↳ QReductionProof
                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                            ↳ Rewriting
                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                ↳ Rewriting
                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                    ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                        ↳ Instantiation
                                                                                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                                                                                            ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                                                                                ↳ Instantiation
                                                                                                                                                                                                                                                                                                                  ↳ QDP
                                                                                                                                                                                                                                                                                                                    ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                        ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                          ↳ AND
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                                                                                                                        ↳ UsableRulesProof
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)

The TRS R consists of the following rules:

new_primPlusNat1(Zero) → Zero
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Zero, Zero) → Zero

The set Q consists of the following terms:

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

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

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

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

new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, ba)

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

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

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

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



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

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

new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), ba) → new_mkVBalBranch3MkVBalBranch162(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ 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_splitGT3(True, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, False, h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, False, h)
new_splitGT3(False, ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, 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 2 SCCs.

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

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

new_splitGT3(False, ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, True, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                              ↳ QDP

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

new_splitGT3(True, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, False, h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, False, 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
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ LetRed
                    ↳ HASKELL
                      ↳ NumRed
                        ↳ HASKELL
                          ↳ Narrow
                            ↳ AND
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                                ↳ QDPSizeChangeProof

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

new_minusFM(Branch(ywv30, ywv31, ywv32, ywv33, ywv34), Branch(ywv40, ywv41, ywv42, ywv43, ywv44), h, ba) → new_minusFM(new_splitLT30(ywv30, ywv31, ywv32, ywv33, ywv34, ywv40, h), ywv43, h, ba)
new_minusFM(Branch(ywv30, ywv31, ywv32, ywv33, ywv34), Branch(ywv40, ywv41, ywv42, ywv43, ywv44), h, ba) → new_minusFM(new_splitGT30(ywv30, ywv31, ywv32, ywv33, ywv34, ywv40, h), ywv44, h, ba)

The TRS R consists of the following rules:

new_mkVBalBranch3MkVBalBranch1103(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1168(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1151(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Zero), be) → new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch7(ywv31, EmptyFM, ywv34, h) → new_addToFM(ywv34, ywv31, h)
new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Zero, be) → new_mkVBalBranch3MkVBalBranch1118(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch198(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkBalBranch6MkBalBranch015(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv10070), bb, bc) → new_mkBalBranch6MkBalBranch018(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, ywv10070, bb, bc)
new_mkVBalBranch3MkVBalBranch1125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv71700)), h) → new_mkVBalBranch3MkVBalBranch1128(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1162(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be) → new_mkBalBranch(ywv1054, ywv1055, ywv1057, new_mkVBalBranch9(ywv1064, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, be), ty_Bool, be)
new_splitLT30(True, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, False, h) → new_splitLT30(ywv330, ywv331, ywv332, ywv333, ywv334, False, h)
new_mkVBalBranch3MkVBalBranch1100(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2620), h) → new_mkVBalBranch3MkVBalBranch1147(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch223(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1180(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1148(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv62400)), h) → new_mkVBalBranch3MkVBalBranch1187(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1118(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be) → new_mkVBalBranch3MkVBalBranch1130(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkBalBranch6Size_l(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_sizeFM(ywv714, bb, bc)
new_mkBalBranch6MkBalBranch013(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv91200, Zero, bb, bc) → new_mkBalBranch6MkBalBranch014(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch182(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch415(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch118(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv10470), bb, bc) → new_mkBalBranch6MkBalBranch112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, ywv10470, bb, bc)
new_mkVBalBranch3MkVBalBranch1203(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, Neg(Succ(ywv71800)), h) → new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv71800, ywv5740, h)
new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57300, ywv716000, h)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Pos(Zero), Pos(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch118(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, new_primMulNat2(ywv10340), bb, bc)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch224(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Pos(Succ(ywv91200)), Pos(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch013(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv91200, new_primMulNat2(ywv9130), bb, bc)
new_primMulNat1(ywv163) → new_primPlusNat3(new_primMulNat0(ywv163), Succ(ywv163))
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch231(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv1013000), bh) → new_mkVBalBranch3MkVBalBranch1107(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(ywv2420), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch3MkVBalBranch223(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h)
new_primPlusNat3(Succ(ywv310), Succ(ywv3200)) → Succ(Succ(new_primPlusNat3(ywv310, ywv3200)))
new_mkVBalBranch3MkVBalBranch1180(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Pos(ywv7470), h) → new_mkVBalBranch3MkVBalBranch1145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch33(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv9840), bb, bc) → new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch(ywv40930, ywv40931, ywv714, ywv40934, bb, bc) → new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, new_primPlusInt(new_mkBalBranch6Size_l(ywv40930, ywv40931, ywv40934, ywv714, bb, bc), new_mkBalBranch6Size_r(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)), bb, bc)
new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Succ(ywv1017000), ca) → new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv99300, ywv1017000, ca)
new_mkBalBranch6MkBalBranch37(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv981, bb, bc) → new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1112(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv101900), ywv9940, ca) → new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv101900, ywv9940, ca)
new_mkBalBranch6MkBalBranch0110(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch49(ywv40930, ywv40931, ywv40934, ywv714, Zero, ywv79800, bb, bc) → new_mkBalBranch6MkBalBranch414(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, Succ(ywv101100), bb, bc) → new_mkBalBranch6MkBalBranch017(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_splitLT30(True, ywv31, ywv32, ywv33, ywv34, True, h) → ywv33
new_mkVBalBranch3MkVBalBranch1133(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ca) → new_mkVBalBranch3MkVBalBranch1194(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, ca), ca)
new_mkVBalBranch3MkVBalBranch1136(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv66300)), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch5(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch236(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_splitLT30(False, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), EmptyFM, True, h) → new_mkVBalBranch6(ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, new_splitLT4(h), h)
new_mkBalBranch6MkBalBranch41(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv867, bb, bc) → new_mkBalBranch6MkBalBranch412(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv867, bb, bc)
new_mkVBalBranch3MkVBalBranch1164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Neg(ywv10130), bh) → new_mkVBalBranch3MkVBalBranch1170(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch236(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h) → new_mkBalBranch(ywv200, ywv201, ywv203, new_mkVBalBranch7(ywv31, ywv204, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h), ty_Bool, h)
new_primPlusNat3(Zero, Succ(ywv3200)) → Succ(ywv3200)
new_primPlusNat3(Succ(ywv310), Zero) → Succ(ywv310)
new_mkVBalBranch3MkVBalBranch230(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv10660), be) → new_mkBalBranch(ywv1059, ywv1060, new_mkVBalBranch6(ywv1064, ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058, ywv1062, be), ywv1063, ty_Bool, be)
new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv912000), Succ(ywv101100), bb, bc) → new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv912000, ywv101100, bb, bc)
new_mkVBalBranch3MkVBalBranch1203(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, Pos(ywv7180), h) → new_mkVBalBranch3MkVBalBranch1154(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_primPlusInt(Pos(ywv4190), Pos(ywv3980)) → Pos(new_primPlusNat3(ywv4190, ywv3980))
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Neg(Zero), Pos(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch019(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_primMulNat2(ywv9130), bb, bc)
new_mkBalBranch6MkBalBranch112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, ywv103300, bb, bc) → new_mkBalBranch6MkBalBranch114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch220(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv718000, ywv57400, h)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1102(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkBalBranch6MkBalBranch111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, EmptyFM, bb, bc) → error([])
new_mkVBalBranch3MkVBalBranch1131(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(ywv9890), ca) → new_mkVBalBranch3MkVBalBranch1133(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), ca)
new_mkBalBranch6MkBalBranch5(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBranch(Zero, ywv40930, ywv40931, ywv714, ywv40934, bb, bc)
new_mkBalBranch6MkBalBranch314(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv9870), bb, bc) → new_mkBalBranch6MkBalBranch35(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Neg(Succ(ywv103300)), Neg(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch115(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, new_primMulNat2(ywv10340), bb, bc)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Pos(Succ(ywv103300)), Neg(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch1113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, new_primMulNat2(ywv10340), bb, bc)
new_mkVBalBranch3MkVBalBranch232(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Succ(ywv9780), ca) → new_mkVBalBranch3MkVBalBranch232(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9770, ywv9780, ca)
new_mkVBalBranch3MkVBalBranch192(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, Pos(Succ(ywv70600)), h) → new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, ywv70600, h)
new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch199(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57100)), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch8(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch185(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch186(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, Zero, bb, bc) → new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch31(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv9860), ywv90900, bb, bc) → new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, ywv9860, ywv90900, bb, bc)
new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch1159(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_primPlusNat1(Succ(ywv62000)) → Succ(Succ(new_primPlusNat1(ywv62000)))
new_mkBalBranch6MkBalBranch011(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, EmptyFM, ywv409344, ywv714, bb, bc) → error([])
new_mkVBalBranch3MkVBalBranch233(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch234(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(ywv90900)), Pos(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch312(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, new_primMulNat(ywv9100), bb, bc)
new_mkBalBranch6MkBalBranch117(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, Zero, bb, bc) → new_mkBalBranch6MkBalBranch1110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, EmptyFM, ywv714, bb, bc) → error([])
new_mkVBalBranch3MkVBalBranch1140(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Zero), bh) → new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd) → new_mkVBalBranch3MkVBalBranch1134(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Pos(Zero), Neg(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch016(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_primMulNat2(ywv9130), bb, bc)
new_mkVBalBranch3MkVBalBranch1120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71500)), h) → new_mkVBalBranch3MkVBalBranch1166(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1156(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1196(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1200(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Zero), bd) → new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1196(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), ty_Bool, h)
new_mkBranch(ywv1039, ywv1040, ywv1041, ywv1042, ywv1043, cb, cc) → Branch(ywv1040, ywv1041, new_primPlusInt(new_primPlusInt(Pos(Succ(Zero)), new_sizeFM(ywv1042, cb, cc)), new_sizeFM(ywv1043, cb, cc)), ywv1042, ywv1043)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkBalBranch(ywv240, ywv241, new_mkVBalBranch6(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv243, h), ywv244, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1187(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch9(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h), ty_Bool, h)
new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, EmptyFM, bb, bc) → error([])
new_mkBalBranch6MkBalBranch44(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(ywv2420), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch237(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h)
new_primPlusNat1(Zero) → Zero
new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch1167(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch10(ywv842, EmptyFM, ywv837, ywv838, ywv839, ywv840, ywv841, bd) → new_addToFM0(ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch194(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1182(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1161(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, be) → new_mkVBalBranch3MkVBalBranch1193(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, be), be)
new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Zero, h) → new_mkVBalBranch3MkVBalBranch194(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_splitGT(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), h) → new_splitGT30(ywv330, ywv331, ywv332, ywv333, ywv334, False, h)
new_mkVBalBranch3MkVBalBranch192(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, Neg(ywv7060), h) → new_mkVBalBranch3MkVBalBranch194(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1151(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107300)), be) → new_mkVBalBranch3MkVBalBranch1162(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_splitGT30(True, ywv31, ywv32, ywv33, ywv34, True, h) → ywv34
new_mkVBalBranch3MkVBalBranch1147(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Pos(ywv6230), h) → new_mkVBalBranch3MkVBalBranch1187(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch117(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, Succ(ywv10450), bb, bc) → new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv10450, bb, bc)
new_mkVBalBranch3MkVBalBranch1126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch8(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch238(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Succ(ywv9640), bh) → new_mkBalBranch(ywv957, ywv958, new_mkVBalBranch7(ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ywv960, bh), ywv961, ty_Bool, bh)
new_mkVBalBranch3MkVBalBranch1125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1127(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch36(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBranch(Succ(Zero), ywv40930, ywv40931, ywv714, ywv40934, bb, bc)
new_mkVBalBranch3MkVBalBranch1138(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv664000), Succ(ywv26500), h) → new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv664000, ywv26500, h)
new_mkBalBranch6Size_r(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_sizeFM(ywv40934, bb, bc)
new_splitLT4(h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch1145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(ywv3420), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch231(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch1104(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1168(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch182(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch230(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Zero, be) → new_mkVBalBranch3MkVBalBranch219(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_splitLT(EmptyFM, h) → new_splitLT4(h)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkVBalBranch3MkVBalBranch230(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv24200, ywv1280, h)
new_mkVBalBranch3MkVBalBranch1111(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Zero), ca) → new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv718000), Zero, h) → new_mkVBalBranch3MkVBalBranch1156(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1165(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101400)), bh) → new_mkVBalBranch3MkVBalBranch1108(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv101400, bh)
new_mkBalBranch6MkBalBranch412(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, Zero, bb, bc) → new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch42(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv868, bb, bc) → new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ywv7140, ywv7141, ywv7143, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ywv40930, ywv40931, ywv7144, ywv40934, bb, bc), bb, bc)
new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, Branch(ywv7140, ywv7141, ywv7142, ywv7143, ywv7144), bb, bc) → new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, new_sizeFM(ywv7144, bb, bc), new_sizeFM(ywv7143, bb, bc), bb, bc)
new_mkVBalBranch3MkVBalBranch233(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Zero, bd) → new_mkVBalBranch3MkVBalBranch234(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1107(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh) → new_mkBalBranch(ywv952, ywv953, ywv955, new_mkVBalBranch7(ywv962, ywv956, Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), bh), ty_Bool, bh)
new_mkVBalBranch3MkVBalBranch1101(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1121(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1202(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch1195(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Zero, ca) → new_mkVBalBranch3MkVBalBranch1114(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1166(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch8(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1183(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9920), bh) → new_mkVBalBranch3MkVBalBranch1106(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, bh), bh)
new_mkBalBranch6MkBalBranch116(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv10520), bb, bc) → new_mkBalBranch6MkBalBranch117(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv10520, Zero, bb, bc)
new_mkVBalBranch3MkVBalBranch1161(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10680), be) → new_mkVBalBranch3MkVBalBranch1116(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, be), be)
new_mkVBalBranch5(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch30(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h)
new_mkVBalBranch3MkVBalBranch225(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h) → new_mkBalBranch(ywv200, ywv201, ywv203, new_mkVBalBranch7(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h), ty_Bool, h)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Neg(Succ(ywv91200)), Neg(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch018(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_primMulNat2(ywv9130), ywv91200, bb, bc)
new_mkVBalBranch3MkVBalBranch1198(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Neg(ywv10170), ca) → new_mkVBalBranch3MkVBalBranch1114(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1101(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv57200)), h) → new_mkVBalBranch3MkVBalBranch1122(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1198(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Pos(ywv10170), ca) → new_mkVBalBranch3MkVBalBranch1195(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, ywv10170, ca)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1101(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), ty_Bool, h)
new_primMulNat2(Succ(ywv91300)) → new_primPlusNat3(new_primPlusNat3(Zero, Succ(ywv91300)), Succ(ywv91300))
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Pos(Zero), Neg(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch33(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, ywv202, ywv203, ywv204), EmptyFM, h) → new_addToFM(Branch(ywv200, ywv201, ywv202, ywv203, ywv204), ywv31, h)
new_mkBalBranch6MkBalBranch412(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, Succ(ywv8670), bb, bc) → new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv8670, bb, bc)
new_mkVBalBranch3MkVBalBranch1101(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57200)), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch5(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkBalBranch6MkBalBranch49(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv8720), ywv79800, bb, bc) → new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, ywv8720, ywv79800, bb, bc)
new_mkBalBranch6MkBalBranch46(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv872, bb, bc) → new_mkBalBranch6MkBalBranch49(ywv40930, ywv40931, ywv40934, ywv714, ywv872, ywv79800, bb, bc)
new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, Zero, Succ(ywv86700), bb, bc) → new_mkBalBranch6MkBalBranch414(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch30(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv9820), bb, bc) → new_mkBalBranch6MkBalBranch31(ywv40930, ywv40931, ywv40934, ywv714, Zero, ywv9820, bb, bc)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Pos(Zero), Pos(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch43(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv7990), bb, bc)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch1137(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch1102(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1109(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch015(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_addToFM_C2(EmptyFM, ywv31, h) → Branch(True, ywv31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkBalBranch6MkBalBranch48(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv8740), bb, bc) → new_mkBalBranch6MkBalBranch412(ywv40930, ywv40931, ywv40934, ywv714, ywv8740, Zero, bb, bc)
new_mkVBalBranch3MkVBalBranch184(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch185(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1132(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ca) → new_mkVBalBranch3MkVBalBranch1111(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, ca), ca)
new_splitLT30(False, ywv31, ywv32, EmptyFM, ywv34, True, h) → new_addToFM_C1(new_splitLT(ywv34, h), ywv31, h)
new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, Succ(ywv104500), bb, bc) → new_mkBalBranch6MkBalBranch114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch1102(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57500)), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch8(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1139(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), ywv343, h), ywv344, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch1155(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch237(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch226(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h)
new_addToFM(ywv34, ywv31, h) → new_addToFM_C2(ywv34, ywv31, h)
new_mkVBalBranch3MkVBalBranch186(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), ty_Bool, h)
new_mkBalBranch6MkBalBranch43(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv8690), bb, bc) → new_mkBalBranch6MkBalBranch49(ywv40930, ywv40931, ywv40934, ywv714, Zero, ywv8690, bb, bc)
new_mkVBalBranch3MkVBalBranch1111(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv101800)), ca) → new_mkVBalBranch3MkVBalBranch1112(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv101800, ca)
new_mkVBalBranch3MkVBalBranch232(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9770), Zero, ca) → new_mkVBalBranch3MkVBalBranch227(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Pos(Succ(ywv103300)), Pos(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch1112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, new_primMulNat2(ywv10340), bb, bc)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(ywv90900)), Neg(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch37(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch3MkVBalBranch198(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5700), h) → new_mkVBalBranch3MkVBalBranch192(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch236(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv343, ywv344, ywv31, h)
new_splitLT30(False, ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_mkVBalBranch6(ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, new_splitLT30(ywv340, ywv341, ywv342, ywv343, ywv344, True, h), h)
new_mkVBalBranch3MkVBalBranch1117(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, Zero, be) → new_mkVBalBranch3MkVBalBranch1118(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1115(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch195(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1183(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, bh) → new_mkVBalBranch3MkVBalBranch1140(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, bh), bh)
new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch1127(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1127(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1138(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(ywv3420), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch224(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h)
new_mkBalBranch6MkBalBranch31(ywv40930, ywv40931, ywv40934, ywv714, Zero, ywv90900, bb, bc) → new_mkBalBranch6MkBalBranch35(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1119(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca) → new_mkBalBranch(ywv966, ywv967, ywv969, new_mkVBalBranch7(ywv976, ywv970, Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ca), ty_Bool, ca)
new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ca) → new_sizeFM(Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, ca)
new_splitGT30(True, ywv31, ywv32, ywv33, ywv34, False, h) → new_mkVBalBranch7(ywv31, new_splitGT(ywv33, h), ywv34, h)
new_mkVBalBranch3MkVBalBranch1108(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv101500), ywv9920, bh) → new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101500, ywv9920, bh)
new_mkBalBranch6MkBalBranch38(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv9880), bb, bc) → new_mkBalBranch6MkBalBranch39(ywv40930, ywv40931, ywv40934, ywv714, ywv9880, Zero, bb, bc)
new_mkVBalBranch3MkVBalBranch1194(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv102000)), ca) → new_mkVBalBranch3MkVBalBranch1195(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv102000, Zero, ca)
new_mkVBalBranch3MkVBalBranch191(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(ywv10670), be) → new_mkVBalBranch3MkVBalBranch1149(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), be)
new_mkVBalBranch3MkVBalBranch1182(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1165(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(Succ(ywv101400)), bh) → new_mkVBalBranch3MkVBalBranch1170(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Neg(Zero), Pos(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch47(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv7990), bb, bc)
new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, Zero, Zero, bb, bc) → new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1135(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1197(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1137(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2150), h) → new_mkBalBranch(ywv200, ywv201, ywv203, new_mkVBalBranch7(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Bool, h)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1197(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Succ(ywv74800)), h) → new_mkVBalBranch3MkVBalBranch1144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Neg(Zero), Neg(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch38(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch3MkVBalBranch188(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd) → new_mkVBalBranch3MkVBalBranch1134(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv1033000), Succ(ywv104500), bb, bc) → new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv1033000, ywv104500, bb, bc)
new_mkBalBranch6MkBalBranch016(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch233(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv8430), Succ(ywv8440), bd) → new_mkVBalBranch3MkVBalBranch233(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv8430, ywv8440, bd)
new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv798000), Succ(ywv86700), bb, bc) → new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, ywv798000, ywv86700, bb, bc)
new_mkBalBranch6MkBalBranch51(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, new_mkBalBranch6Size_r(ywv40930, ywv40931, ywv40934, ywv714, bb, bc), new_mkBalBranch6Size_l(ywv40930, ywv40931, ywv40934, ywv714, bb, bc), bb, bc)
new_mkVBalBranch3MkVBalBranch1192(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv107200), ywv10690, be) → new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107200, ywv10690, be)
new_mkVBalBranch3MkVBalBranch1103(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv2650), h) → new_mkVBalBranch3MkVBalBranch1158(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1151(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(Zero), be) → new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1153(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv71900)), h) → new_mkVBalBranch3MkVBalBranch1156(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch238(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Succ(ywv9640), bh) → new_mkVBalBranch3MkVBalBranch238(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9630, ywv9640, bh)
new_mkBalBranch6MkBalBranch48(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71700)), h) → new_mkVBalBranch3MkVBalBranch1126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Pos(Succ(ywv91200)), Neg(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch014(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1173(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(ywv9830), bh) → new_mkVBalBranch3MkVBalBranch1163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), bh)
new_mkVBalBranch3MkVBalBranch1145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch9(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1202(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5740), h) → new_mkVBalBranch3MkVBalBranch1203(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(Zero)), bb, bc) → new_mkBalBranch6MkBalBranch5(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1106(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Neg(ywv10150), bh) → new_mkVBalBranch3MkVBalBranch1108(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv10150, ywv9920, bh)
new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv1033000), Zero, bb, bc) → new_mkBalBranch6MkBalBranch1110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Neg(Succ(ywv90900)), Pos(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch313(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch3MkVBalBranch1130(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv1064, Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), Branch(ywv1059, ywv1060, Neg(Succ(ywv1061)), ywv1062, ywv1063), ty_Bool, be)
new_addToFM00(ywv341, ywv31, h) → ywv31
new_mkBalBranch6MkBalBranch313(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv985, bb, bc) → new_mkBalBranch6MkBalBranch35(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1194(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Succ(ywv102000)), ca) → new_mkVBalBranch3MkVBalBranch1119(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1180(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, Neg(Succ(ywv74700)), h) → new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv74700, ywv6210, h)
new_mkVBalBranch8(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv243, ywv244, h) → new_mkVBalBranch30(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Neg(Zero), Pos(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch1115(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, new_primMulNat2(ywv10340), bb, bc)
new_mkVBalBranch3MkVBalBranch1158(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Neg(Succ(ywv66400)), h) → new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv66400, ywv2650, h)
new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, Zero, bb, bc) → new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1191(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Pos(ywv10370), bd) → new_mkVBalBranch3MkVBalBranch189(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1177(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch184(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv57600)), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch5(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch199(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch196(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_primMinusNat0(Succ(ywv41900), Zero) → Pos(Succ(ywv41900))
new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch1166(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_sizeFM(EmptyFM, bf, bg) → Pos(Zero)
new_mkBalBranch6MkBalBranch017(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc) → new_mkBranch(Succ(Succ(Zero)), ywv409340, ywv409341, new_mkBranch(Succ(Succ(Succ(Zero))), ywv40930, ywv40931, ywv714, ywv409343, bb, bc), ywv409344, bb, bc)
new_mkVBalBranch3MkVBalBranch1193(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(Zero), be) → new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1121(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1122(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Succ(ywv1035000), bd) → new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv97900, ywv1035000, bd)
new_mkVBalBranch3MkVBalBranch1112(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, ywv9940, ca) → new_mkVBalBranch3MkVBalBranch1119(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1147(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1187(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1184(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv5730), h) → new_mkVBalBranch3MkVBalBranch1185(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1147(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2620, Neg(Succ(ywv62300)), h) → new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv62300, ywv2620, h)
new_mkVBalBranch3MkVBalBranch1185(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1128(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch225(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Zero, ywv343, ywv344, ywv31, h)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch184(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkBalBranch6MkBalBranch014(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch011(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1100(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1148(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Pos(Zero), bb, bc) → new_mkBalBranch6MkBalBranch5(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv770), h) → new_mkVBalBranch3MkVBalBranch238(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv770, ywv34200, h)
new_mkBalBranch6MkBalBranch33(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_splitGT30(False, ywv31, ywv32, ywv33, EmptyFM, True, h) → new_emptyFM(h)
new_primPlusNat3(Zero, Zero) → Zero
new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be) → new_mkVBalBranch3MkVBalBranch1130(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1123(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h) → new_mkBalBranch(ywv200, ywv201, ywv203, new_mkVBalBranch7(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Bool, h)
new_mkBalBranch6MkBalBranch1110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc) → new_mkBalBranch6MkBalBranch111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Neg(Succ(ywv90900)), Neg(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch310(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch3MkVBalBranch1101(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1121(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_primMulNat2(Zero) → Zero
new_mkVBalBranch3MkVBalBranch184(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv57600)), h) → new_mkVBalBranch3MkVBalBranch186(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1184(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1178(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(Succ(ywv104400)), bd) → new_mkVBalBranch3MkVBalBranch1179(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv104400, Zero, bd)
new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv106800), Succ(ywv1070000), be) → new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv106800, ywv1070000, be)
new_mkVBalBranch3MkVBalBranch1139(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2300), h) → new_mkBalBranch(ywv200, ywv201, ywv203, new_mkVBalBranch7(ywv31, ywv204, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch191(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(ywv10670), be) → new_mkVBalBranch3MkVBalBranch1161(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_primMulNat(ywv10670), be)
new_mkVBalBranch3MkVBalBranch232(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, ca) → new_mkVBalBranch3MkVBalBranch227(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1197(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv74800)), h) → new_mkVBalBranch3MkVBalBranch1145(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch220(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch198(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch6(ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, Branch(ywv240, ywv241, ywv242, ywv243, ywv244), h) → new_mkVBalBranch30(ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h)
new_splitLT30(False, ywv31, ywv32, ywv33, ywv34, False, h) → ywv33
new_mkVBalBranch3MkVBalBranch1102(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv57500)), h) → new_mkVBalBranch3MkVBalBranch1110(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch39(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, Zero, bb, bc) → new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_addToFM_C2(Branch(True, ywv341, ywv342, ywv343, ywv344), ywv31, h) → Branch(True, new_addToFM00(ywv341, ywv31, h), ywv342, ywv343, ywv344)
new_mkBalBranch6MkBalBranch43(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1185(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, Pos(Succ(ywv71600)), h) → new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, ywv71600, h)
new_mkVBalBranch10(ywv842, Branch(ywv8360, ywv8361, ywv8362, ywv8363, ywv8364), ywv837, ywv838, ywv839, ywv840, ywv841, bd) → new_mkVBalBranch30(ywv842, ywv8360, ywv8361, ywv8362, ywv8363, ywv8364, ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841, bd)
new_mkVBalBranch3MkVBalBranch231(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h), ywv344, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1154(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch5(ywv31, ywv334, ywv240, ywv241, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1199(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, Neg(ywv10350), bd) → new_mkVBalBranch3MkVBalBranch188(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Neg(Succ(ywv91200)), Pos(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch017(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch1170(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh) → new_mkVBalBranch3MkVBalBranch1172(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch1140(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(Zero), bh) → new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), ywv343, h), ywv344, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1114(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca) → new_mkVBalBranch3MkVBalBranch1157(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1153(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1155(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch238(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, Succ(ywv34200), h)
new_mkVBalBranch3MkVBalBranch1178(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Zero), bd) → new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1199(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, Pos(ywv10350), bd) → new_mkVBalBranch3MkVBalBranch1179(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, ywv10350, bd)
new_primMulNat(Zero) → Zero
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Neg(Succ(ywv79800)), Pos(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch45(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, new_primMulNat(ywv7990), bb, bc)
new_mkVBalBranch3MkVBalBranch1116(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, Pos(ywv10700), be) → new_mkVBalBranch3MkVBalBranch1117(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, ywv10700, be)
new_addToFM_C1(Branch(False, ywv251, ywv252, ywv253, ywv254), ywv31, h) → Branch(False, new_addToFM00(ywv251, ywv31, h), ywv252, ywv253, ywv254)
new_mkVBalBranch3MkVBalBranch226(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1136(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch238(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9630), Zero, bh) → new_mkVBalBranch3MkVBalBranch235(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch9(ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv240, ywv241, ywv24200, ywv243, ywv244, h) → new_mkVBalBranch30(ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h)
new_primPlusInt(Neg(ywv4190), Pos(ywv3980)) → new_primMinusNat0(ywv3980, ywv4190)
new_primPlusInt(Pos(ywv4190), Neg(ywv3980)) → new_primMinusNat0(ywv4190, ywv3980)
new_splitLT(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitLT30(ywv340, ywv341, ywv342, ywv343, ywv344, True, h)
new_mkBalBranch6MkBalBranch112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv10500), ywv103300, bb, bc) → new_mkBalBranch6MkBalBranch113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv10500, ywv103300, bb, bc)
new_mkBalBranch6MkBalBranch1113(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv1046, bb, bc) → new_mkBalBranch6MkBalBranch1110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch1164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Pos(ywv10130), bh) → new_mkVBalBranch3MkVBalBranch1142(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, ywv10130, bh)
new_addToFM_C1(EmptyFM, ywv31, h) → Branch(False, ywv31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkBalBranch6MkBalBranch019(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv10090), bb, bc) → new_mkBalBranch6MkBalBranch017(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Neg(Zero), Neg(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch116(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, new_primMulNat2(ywv10340), bb, bc)
new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv798000), Zero, bb, bc) → new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_splitGT30(False, ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), True, h) → new_splitGT30(ywv340, ywv341, ywv342, ywv343, ywv344, True, h)
new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv747000), Zero, h) → new_mkVBalBranch3MkVBalBranch1144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Neg(Zero), Pos(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch314(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv9100), bb, bc)
new_mkVBalBranch3MkVBalBranch1173(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(ywv9830), bh) → new_mkVBalBranch3MkVBalBranch1183(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_primMulNat(ywv9830), bh)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkVBalBranch3MkVBalBranch1202(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1153(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1111(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Zero), ca) → new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkBalBranch6MkBalBranch016(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv10080), bb, bc) → new_mkBalBranch6MkBalBranch014(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1133(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9940), ca) → new_mkVBalBranch3MkVBalBranch1189(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, ca), ca)
new_mkVBalBranch3MkVBalBranch1140(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(Succ(ywv101600)), bh) → new_mkVBalBranch3MkVBalBranch1142(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv101600, Zero, bh)
new_mkVBalBranch3MkVBalBranch223(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv2420, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv240, ywv241, new_mkVBalBranch6(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h), ywv244, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1176(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9900), bd) → new_mkVBalBranch3MkVBalBranch1191(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, bd), bd)
new_mkVBalBranch3MkVBalBranch1204(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv57400), h) → new_mkVBalBranch3MkVBalBranch1154(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1189(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Neg(ywv10190), ca) → new_mkVBalBranch3MkVBalBranch1112(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv10190, ywv9940, ca)
new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca) → new_mkVBalBranch3MkVBalBranch1157(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1136(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv66300)), h) → new_mkVBalBranch3MkVBalBranch1177(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1151(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(Succ(ywv107300)), be) → new_mkVBalBranch3MkVBalBranch1117(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv107300, Zero, be)
new_mkBalBranch6MkBalBranch30(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1117(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, Succ(ywv107000), be) → new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, ywv107000, be)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1100(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat1(ywv24200), h)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(Succ(Succ(ywv7200000)))), bb, bc) → new_mkBalBranch6MkBalBranch51(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch195(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Succ(ywv1260), h) → new_mkVBalBranch3MkVBalBranch233(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv1260, ywv24200, h)
new_mkVBalBranch3MkVBalBranch234(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd) → new_mkVBalBranch3MkVBalBranch1174(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_mkVBalBranch3Size_r(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, bd), bd)
new_mkVBalBranch3MkVBalBranch1149(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, be) → new_mkVBalBranch3MkVBalBranch1151(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, be), be)
new_mkVBalBranch3MkVBalBranch199(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch196(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv1017000), ca) → new_mkVBalBranch3MkVBalBranch1119(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Pos(Zero), Neg(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch44(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv7990), bb, bc)
new_primMulNat0(ywv6200) → new_primPlusNat2(Succ(new_primPlusNat2(new_primPlusNat1(ywv6200), ywv6200)), Succ(ywv6200))
new_mkVBalBranch3MkVBalBranch1163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, bh) → new_mkVBalBranch3MkVBalBranch1165(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, bh), bh)
new_mkVBalBranch3MkVBalBranch1155(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1196(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1110(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv747000), Succ(ywv62100), h) → new_mkVBalBranch3MkVBalBranch1143(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv747000, ywv62100, h)
new_mkVBalBranch3MkVBalBranch238(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch235(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch224(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch225(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv3420, ywv343, ywv344, ywv31, h)
new_splitLT30(True, ywv31, ywv32, EmptyFM, ywv34, False, h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Zero, h) → new_mkVBalBranch3MkVBalBranch1190(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch232(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Succ(ywv9780), ca) → new_mkBalBranch(ywv971, ywv972, new_mkVBalBranch7(ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ywv974, ca), ywv975, ty_Bool, ca)
new_mkBalBranch6MkBalBranch0110(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv10100), bb, bc) → new_mkBalBranch6MkBalBranch013(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv10100, Zero, bb, bc)
new_mkVBalBranch3Size_r(ywv578, ywv579, ywv580, ywv581, ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, cd) → new_sizeFM(Branch(ywv583, ywv584, Pos(Succ(ywv585)), ywv586, ywv587), ty_Bool, cd)
new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv1035000), bd) → new_mkVBalBranch3MkVBalBranch189(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_splitGT(EmptyFM, h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch018(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, ywv91200, bb, bc) → new_mkBalBranch6MkBalBranch017(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1148(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1190(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch230(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10650), Succ(ywv10660), be) → new_mkVBalBranch3MkVBalBranch230(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10650, ywv10660, be)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch232(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv34200), Zero, h)
new_primMulNat(Succ(ywv32800)) → new_primPlusNat3(new_primMulNat0(ywv32800), Succ(ywv32800))
new_mkVBalBranch5(ywv31, EmptyFM, ywv240, ywv241, ywv243, ywv244, h) → new_addToFM0(ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch35(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch36(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1104(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1105(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Pos(Zero), Neg(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch119(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, new_primMulNat2(ywv10340), bb, bc)
new_mkVBalBranch3MkVBalBranch1174(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(ywv9110), bd) → new_mkVBalBranch3MkVBalBranch1175(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), bd)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch220(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1200(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv103600)), bd) → new_mkVBalBranch3MkVBalBranch1171(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv103600, bd)
new_mkVBalBranch3MkVBalBranch1146(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Succ(ywv1070000), be) → new_mkVBalBranch3MkVBalBranch1162(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1168(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch182(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1167(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1182(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch013(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv91200, Succ(ywv10110), bb, bc) → new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv91200, ywv10110, bb, bc)
new_mkVBalBranch3MkVBalBranch1179(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, Zero, bd) → new_mkVBalBranch3MkVBalBranch188(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Neg(Succ(ywv72000)), bb, bc) → new_mkBalBranch6MkBalBranch5(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(Succ(Zero))), bb, bc) → new_mkBalBranch6MkBalBranch51(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, Pos(Zero), Pos(ywv9100), bb, bc) → new_mkBalBranch6MkBalBranch30(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv9100), bb, bc)
new_mkBalBranch6MkBalBranch310(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv986, bb, bc) → new_mkBalBranch6MkBalBranch31(ywv40930, ywv40931, ywv40934, ywv714, ywv986, ywv90900, bb, bc)
new_sizeFM(Branch(ywv2950, ywv2951, ywv2952, ywv2953, ywv2954), bf, bg) → ywv2952
new_mkBalBranch6MkBalBranch118(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, bb, bc) → new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch1194(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(Zero), ca) → new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv623000), Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv623000, ywv26200, h)
new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, Zero, bh) → new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch1128(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1138(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch019(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv623000), Zero, h) → new_mkVBalBranch3MkVBalBranch1115(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch47(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv97900), Zero, bd) → new_mkVBalBranch3MkVBalBranch188(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch6(ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, EmptyFM, h) → new_addToFM0(ywv330, ywv331, ywv332, ywv333, ywv334, ywv31, h)
new_mkVBalBranch3MkVBalBranch1160(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv664000), Zero, h) → new_mkVBalBranch3MkVBalBranch1169(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch233(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv24200), h)
new_mkVBalBranch3MkVBalBranch1116(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10680, Neg(ywv10700), be) → new_mkVBalBranch3MkVBalBranch1118(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1122(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Zero), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1136(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1186(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch183(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1108(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Zero, ywv9920, bh) → new_mkVBalBranch3MkVBalBranch1107(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch1186(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1177(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch192(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5700, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch194(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, Branch(ywv71440, ywv71441, ywv71442, ywv71443, ywv71444), bb, bc) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), ywv71440, ywv71441, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), ywv7140, ywv7141, ywv7143, ywv71443, bb, bc), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), ywv40930, ywv40931, ywv71444, ywv40934, bb, bc), bb, bc)
new_primPlusNat2(ywv31, Succ(ywv320)) → Succ(Succ(new_primPlusNat3(ywv31, ywv320)))
new_mkVBalBranch3MkVBalBranch1193(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Succ(ywv107100)), be) → new_mkVBalBranch3MkVBalBranch1192(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv107100, be)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv242, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv33200), Succ(ywv33200)), h)
new_mkBalBranch6MkBalBranch47(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv8730), bb, bc) → new_mkBalBranch6MkBalBranch414(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch227(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca) → new_mkVBalBranch3MkVBalBranch1131(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_mkVBalBranch3Size_r0(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ca), ca)
new_mkVBalBranch8(ywv31, EmptyFM, ywv240, ywv241, ywv243, ywv244, h) → new_addToFM0(ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, h)
new_addToFM0(ywv330, ywv331, ywv332, ywv333, ywv334, ywv31, h) → new_addToFM_C1(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv31, h)
new_mkVBalBranch3MkVBalBranch1174(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(ywv9110), bd) → new_mkVBalBranch3MkVBalBranch1176(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_primMulNat(ywv9110), bd)
new_mkVBalBranch3MkVBalBranch1106(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9920, Pos(ywv10150), bh) → new_mkVBalBranch3MkVBalBranch1107(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), ywv343, h), ywv344, ty_Bool, h)
new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc) → new_mkBalBranch6MkBalBranch111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_addToFM_C2(Branch(False, ywv341, ywv342, ywv343, ywv344), ywv31, h) → new_mkBalBranch(False, ywv341, ywv343, new_addToFM_C2(ywv344, ywv31, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1197(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1104(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1167(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch1111(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Neg(Succ(ywv103300)), Pos(ywv10340), bb, bc) → new_mkBalBranch6MkBalBranch1114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, new_primMulNat2(ywv10340), bb, bc)
new_mkVBalBranch3MkVBalBranch1135(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv6210), h) → new_mkVBalBranch3MkVBalBranch1180(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv6210, new_sizeFM(Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch235(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh) → new_mkVBalBranch3MkVBalBranch1173(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, new_mkVBalBranch3Size_r(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, bh), bh)
new_mkVBalBranch3MkVBalBranch1165(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Zero), bh) → new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57000), Succ(ywv706000), h) → new_mkVBalBranch3MkVBalBranch193(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv57000, ywv706000, h)
new_mkVBalBranch3MkVBalBranch1188(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Zero, Succ(ywv26200), h) → new_mkVBalBranch3MkVBalBranch1187(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1165(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Neg(Zero), bh) → new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch1102(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1109(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_primPlusInt(Neg(ywv4190), Neg(ywv3980)) → Neg(new_primPlusNat3(ywv4190, ywv3980))
new_mkVBalBranch3MkVBalBranch1192(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, ywv10690, be) → new_mkVBalBranch3MkVBalBranch1162(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch1158(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1159(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Neg(Zero), Neg(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch0110(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_primMulNat2(ywv9130), bb, bc)
new_mkVBalBranch3MkVBalBranch1134(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv842, Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), Branch(ywv837, ywv838, Pos(Succ(ywv839)), ywv840, ywv841), ty_Bool, bd)
new_mkBalBranch6MkBalBranch314(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch226(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1135(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primPlusNat3(new_primMulNat0(ywv24200), Succ(ywv24200)), h)
new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv912000), Zero, bb, bc) → new_mkBalBranch6MkBalBranch014(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Neg(Zero), Neg(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch48(ywv40930, ywv40931, ywv40934, ywv714, new_primMulNat(ywv7990), bb, bc)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Pos(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch228(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv342, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv20200), Succ(ywv20200)), h)
new_mkVBalBranch3MkVBalBranch1153(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Succ(ywv71900)), h) → new_mkVBalBranch3MkVBalBranch1154(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1141(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh) → new_mkVBalBranch3MkVBalBranch1172(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv909000), Zero, bb, bc) → new_mkBalBranch6MkBalBranch34(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch1115(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, bb, bc) → new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch018(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Succ(ywv10120), ywv91200, bb, bc) → new_mkBalBranch6MkBalBranch0111(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, ywv10120, ywv91200, bb, bc)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), ty_Bool, h)
new_mkBalBranch6MkBalBranch39(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, Succ(ywv9800), bb, bc) → new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv9800, bb, bc)
new_emptyFM(h) → EmptyFM
new_mkVBalBranch3MkVBalBranch1175(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv9790), bd) → new_mkVBalBranch3MkVBalBranch1199(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, bd), bd)
new_mkVBalBranch3MkVBalBranch1109(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1110(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch116(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, bb, bc) → new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch1168(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Succ(ywv67400)), h) → new_mkVBalBranch3MkVBalBranch1169(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch1115(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv10510), bb, bc) → new_mkBalBranch6MkBalBranch114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Pos(Zero), ywv343, ywv344, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Neg(Succ(ywv20200)), ywv203, ywv204), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1111(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Succ(ywv101800)), ca) → new_mkVBalBranch3MkVBalBranch1114(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkBalBranch6MkBalBranch011(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, Branch(ywv4093430, ywv4093431, ywv4093432, ywv4093433, ywv4093434), ywv409344, ywv714, bb, bc) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), ywv4093430, ywv4093431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), ywv40930, ywv40931, ywv714, ywv4093433, bb, bc), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), ywv409340, ywv409341, ywv4093434, ywv409344, bb, bc), bb, bc)
new_mkVBalBranch3MkVBalBranch1200(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(Succ(ywv103600)), bd) → new_mkVBalBranch3MkVBalBranch188(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1148(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Neg(Succ(ywv62400)), h) → new_mkVBalBranch3MkVBalBranch1115(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1159(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch9(ywv31, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, h), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1178(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(Zero), bd) → new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch197(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv240, ywv241, Pos(Zero), ywv243, ywv244), ty_Bool, h)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Neg(Succ(ywv79800)), Neg(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch46(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, new_primMulNat(ywv7990), bb, bc)
new_mkBalBranch6MkBalBranch1114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv1049, bb, bc) → new_mkBalBranch6MkBalBranch114(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, Pos(Zero), Pos(ywv9130), bb, bc) → new_mkBalBranch6MkBalBranch015(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_primMulNat2(ywv9130), bb, bc)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch237(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Succ(ywv24200), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1144(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch1105(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch230(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Succ(ywv24200), Zero, h)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch199(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_sizeFM(Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), ty_Bool, h), h)
new_mkVBalBranch3MkVBalBranch1132(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv9930), ca) → new_mkVBalBranch3MkVBalBranch1198(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, new_sizeFM(Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), ty_Bool, ca), ca)
new_mkVBalBranch3MkVBalBranch182(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch183(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch219(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be) → new_mkVBalBranch3MkVBalBranch191(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, new_mkVBalBranch3Size_r0(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, be), be)
new_mkVBalBranch3MkVBalBranch1149(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Succ(ywv10690), be) → new_mkVBalBranch3MkVBalBranch1150(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, new_sizeFM(Branch(ywv1054, ywv1055, Neg(Succ(ywv1056)), ywv1057, ywv1058), ty_Bool, be), be)
new_mkVBalBranch3MkVBalBranch1194(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Neg(Zero), ca) → new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1105(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), False, ywv31, Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), Branch(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244), ty_Bool, h)
new_mkVBalBranch7(ywv31, Branch(ywv200, ywv201, Neg(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch1139(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primMulNat1(ywv34200), h)
new_mkVBalBranch3MkVBalBranch1168(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Succ(ywv67400)), h) → new_mkVBalBranch3MkVBalBranch1159(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch415(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch311(ywv40930, ywv40931, ywv40934, ywv714, new_mkBalBranch6Size_l(ywv40930, ywv40931, ywv40934, ywv714, bb, bc), new_mkBalBranch6Size_r(ywv40930, ywv40931, ywv40934, ywv714, bb, bc), bb, bc)
new_mkVBalBranch3MkVBalBranch1191(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9900, Neg(ywv10370), bd) → new_mkVBalBranch3MkVBalBranch1171(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv10370, ywv9900, bd)
new_mkVBalBranch3MkVBalBranch1171(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Succ(ywv103700), ywv9900, bd) → new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv103700, ywv9900, bd)
new_mkVBalBranch3MkVBalBranch1200(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Neg(Zero), bd) → new_mkVBalBranch3MkVBalBranch190(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch3MkVBalBranch1157(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv976, Branch(ywv966, ywv967, Neg(Succ(ywv968)), ywv969, ywv970), Branch(ywv971, ywv972, Neg(Succ(ywv973)), ywv974, ywv975), ty_Bool, ca)
new_primMinusNat0(Zero, Succ(ywv39800)) → Neg(Succ(ywv39800))
new_mkVBalBranch3MkVBalBranch1172(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv962, Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), Branch(ywv957, ywv958, Pos(Succ(ywv959)), ywv960, ywv961), ty_Bool, bh)
new_mkVBalBranch3MkVBalBranch1140(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Pos(Succ(ywv101600)), bh) → new_mkVBalBranch3MkVBalBranch1107(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Succ(ywv1013000), bh) → new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv99100, ywv1013000, bh)
new_mkVBalBranch3MkVBalBranch1171(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, ywv9900, bd) → new_mkVBalBranch3MkVBalBranch189(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv240, ywv241, Pos(Succ(ywv24200)), ywv243, ywv244, h) → new_mkBalBranch(ywv240, ywv241, new_mkVBalBranch6(ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv243, h), ywv244, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv99100), Zero, bh) → new_mkVBalBranch3MkVBalBranch1170(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Succ(ywv99300), Zero, ca) → new_mkVBalBranch3MkVBalBranch1114(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkBalBranch6MkBalBranch50(ywv40930, ywv40931, ywv40934, ywv714, Neg(Zero), bb, bc) → new_mkBalBranch6MkBalBranch5(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1142(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Zero, bh) → new_mkVBalBranch3MkVBalBranch1170(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, bh)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Pos(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1184(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, new_primMulNat(Zero), h)
new_mkVBalBranch3MkVBalBranch1158(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, ywv2650, Pos(ywv6640), h) → new_mkVBalBranch3MkVBalBranch1159(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch119(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Succ(ywv10480), bb, bc) → new_mkBalBranch6MkBalBranch1110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv909000), Succ(ywv98000), bb, bc) → new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, ywv909000, ywv98000, bb, bc)
new_mkVBalBranch3MkVBalBranch1185(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5730, Neg(ywv7160), h) → new_mkVBalBranch3MkVBalBranch1128(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch222(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Succ(ywv1280), h) → new_mkBalBranch(ywv240, ywv241, new_mkVBalBranch6(ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv243, h), ywv244, ty_Bool, h)
new_mkBalBranch6MkBalBranch119(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, Zero, bb, bc) → new_mkBalBranch6MkBalBranch110(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, bb, bc)
new_mkVBalBranch3MkVBalBranch1152(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch1123(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch1176(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, bd) → new_mkVBalBranch3MkVBalBranch1178(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, bd), bd)
new_primPlusNat2(ywv31, Zero) → Succ(ywv31)
new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, Branch(ywv409340, ywv409341, ywv409342, ywv409343, ywv409344), ywv714, bb, bc) → new_mkBalBranch6MkBalBranch012(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, new_sizeFM(ywv409343, bb, bc), new_sizeFM(ywv409344, bb, bc), bb, bc)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(ywv79800)), Neg(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch42(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, new_primMulNat(ywv7990), bb, bc)
new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch36(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1203(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, ywv5740, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1154(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1153(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1155(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1189(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9940, Pos(ywv10190), ca) → new_mkVBalBranch3MkVBalBranch1119(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch1137(ywv200, ywv201, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), True, ywv31, Branch(ywv200, ywv201, Pos(Zero), ywv203, ywv204), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1131(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Pos(ywv9890), ca) → new_mkVBalBranch3MkVBalBranch1132(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, new_primMulNat(ywv9890), ca)
new_mkVBalBranch3MkVBalBranch225(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv31, h) → new_mkVBalBranch3MkVBalBranch1152(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, new_primPlusNat3(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_addToFM_C1(Branch(True, ywv251, ywv252, ywv253, ywv254), ywv31, h) → new_mkBalBranch(True, ywv251, new_addToFM_C1(ywv253, ywv31, h), ywv254, ty_Bool, h)
new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, Zero, Zero, ca) → new_mkVBalBranch3MkVBalBranch1113(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ca)
new_mkVBalBranch3MkVBalBranch221(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Neg(Zero), ywv243, ywv244, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch226(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, Zero, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Succ(ywv57300), Zero, h) → new_mkVBalBranch3MkVBalBranch1128(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch414(ywv40930, ywv40931, ywv40934, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch415(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1197(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1104(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1201(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Zero, Succ(ywv716000), h) → new_mkVBalBranch3MkVBalBranch1126(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1152(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, Succ(ywv2440), h) → new_mkVBalBranch3MkVBalBranch1123(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, h)
new_mkVBalBranch3MkVBalBranch1120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Zero), h) → new_mkVBalBranch3MkVBalBranch1167(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1142(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, Succ(ywv101300), bh) → new_mkVBalBranch3MkVBalBranch1181(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, ywv101300, bh)
new_mkVBalBranch3MkVBalBranch229(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344, ywv31, Succ(ywv790), h) → new_mkVBalBranch3MkVBalBranch232(ywv200, ywv201, ywv20200, ywv203, ywv204, ywv340, ywv341, ywv34200, ywv343, ywv344, ywv31, ywv34200, ywv790, h)
new_mkVBalBranch3MkVBalBranch1150(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Neg(ywv10720), be) → new_mkVBalBranch3MkVBalBranch1192(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10720, ywv10690, be)
new_mkVBalBranch3MkVBalBranch1150(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, ywv10690, Pos(ywv10720), be) → new_mkVBalBranch3MkVBalBranch1162(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch199(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv57100)), h) → new_mkVBalBranch3MkVBalBranch197(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch44(ywv40930, ywv40931, ywv40934, ywv714, Succ(ywv8700), bb, bc) → new_mkBalBranch6MkBalBranch410(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1193(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Neg(Succ(ywv107100)), be) → new_mkVBalBranch3MkVBalBranch1118(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkVBalBranch3MkVBalBranch230(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Zero, Zero, be) → new_mkVBalBranch3MkVBalBranch219(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_mkBalBranch6MkBalBranch1112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv1045, bb, bc) → new_mkBalBranch6MkBalBranch117(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv1045, bb, bc)
new_mkVBalBranch3MkVBalBranch196(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch197(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1190(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch195(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch315(ywv40930, ywv40931, ywv40934, ywv714, Zero, Succ(ywv98000), bb, bc) → new_mkBalBranch6MkBalBranch35(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch233(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, Succ(ywv8440), bd) → new_mkBalBranch(ywv837, ywv838, new_mkVBalBranch6(ywv842, ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836, ywv840, bd), ywv841, ty_Bool, bd)
new_mkVBalBranch3MkVBalBranch1179(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, Succ(ywv103500), bd) → new_mkVBalBranch3MkVBalBranch187(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, ywv9790, ywv103500, bd)
new_mkVBalBranch3MkVBalBranch1136(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1186(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkBalBranch6MkBalBranch115(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv103300, ywv1050, bb, bc) → new_mkBalBranch6MkBalBranch112(ywv40930, ywv40931, ywv40934, ywv7140, ywv7141, ywv7142, ywv7143, ywv7144, ywv1050, ywv103300, bb, bc)
new_mkBalBranch6MkBalBranch312(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv980, bb, bc) → new_mkBalBranch6MkBalBranch39(ywv40930, ywv40931, ywv40934, ywv714, ywv90900, ywv980, bb, bc)
new_mkVBalBranch3MkVBalBranch1163(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, Succ(ywv9910), bh) → new_mkVBalBranch3MkVBalBranch1164(ywv952, ywv953, ywv954, ywv955, ywv956, ywv957, ywv958, ywv959, ywv960, ywv961, ywv962, ywv9910, new_sizeFM(Branch(ywv952, ywv953, Pos(Succ(ywv954)), ywv955, ywv956), ty_Bool, bh), bh)
new_mkVBalBranch3MkVBalBranch189(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd) → new_mkBalBranch(ywv832, ywv833, ywv835, new_mkVBalBranch10(ywv842, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, bd), ty_Bool, bd)
new_mkVBalBranch30(ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, h) → new_mkVBalBranch3MkVBalBranch1103(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, new_primMulNat(Succ(ywv24200)), h)
new_mkVBalBranch3MkVBalBranch1175(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Zero, bd) → new_mkVBalBranch3MkVBalBranch1200(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, new_sizeFM(Branch(ywv832, ywv833, Pos(Succ(ywv834)), ywv835, ywv836), ty_Bool, bd), bd)
new_mkBalBranch6MkBalBranch40(ywv40930, ywv40931, ywv40934, ywv714, Pos(Succ(ywv79800)), Pos(ywv7990), bb, bc) → new_mkBalBranch6MkBalBranch41(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, new_primMulNat(ywv7990), bb, bc)
new_mkBalBranch6MkBalBranch413(ywv40930, ywv40931, ywv40934, ywv714, Zero, Zero, bb, bc) → new_mkBalBranch6MkBalBranch411(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch9(ywv31, EmptyFM, ywv240, ywv241, ywv24200, ywv243, ywv244, h) → new_addToFM0(ywv240, ywv241, Neg(Succ(ywv24200)), ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch184(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch185(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1195(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, Succ(ywv101700), ca) → new_mkVBalBranch3MkVBalBranch1124(ywv966, ywv967, ywv968, ywv969, ywv970, ywv971, ywv972, ywv973, ywv974, ywv975, ywv976, ywv9930, ywv101700, ca)
new_splitGT30(False, ywv31, ywv32, ywv33, ywv34, False, h) → ywv34
new_mkBalBranch6MkBalBranch38(ywv40930, ywv40931, ywv40934, ywv714, Zero, bb, bc) → new_mkBalBranch6MkBalBranch32(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1125(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1127(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1120(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, Neg(Succ(ywv71500)), h) → new_mkVBalBranch3MkVBalBranch194(ywv330, ywv331, ywv33200, ywv333, ywv334, ywv240, ywv241, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1169(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h) → new_mkVBalBranch3MkVBalBranch183(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1178(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, Pos(Succ(ywv104400)), bd) → new_mkVBalBranch3MkVBalBranch189(ywv832, ywv833, ywv834, ywv835, ywv836, ywv837, ywv838, ywv839, ywv840, ywv841, ywv842, bd)
new_mkBalBranch6MkBalBranch010(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc) → new_mkBalBranch6MkBalBranch011(ywv40930, ywv40931, ywv409340, ywv409341, ywv409342, ywv409343, ywv409344, ywv714, bb, bc)
new_mkBalBranch6MkBalBranch45(ywv40930, ywv40931, ywv40934, ywv714, ywv79800, ywv871, bb, bc) → new_mkBalBranch6MkBalBranch414(ywv40930, ywv40931, ywv40934, ywv714, bb, bc)
new_mkVBalBranch3MkVBalBranch1148(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, Pos(Zero), h) → new_mkVBalBranch3MkVBalBranch1190(ywv330, ywv331, ywv333, ywv334, ywv240, ywv241, ywv24200, ywv243, ywv244, ywv31, h)
new_mkVBalBranch3MkVBalBranch1193(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, Pos(Zero), be) → new_mkVBalBranch3MkVBalBranch1129(ywv1054, ywv1055, ywv1056, ywv1057, ywv1058, ywv1059, ywv1060, ywv1061, ywv1062, ywv1063, ywv1064, be)
new_primMinusNat0(Succ(ywv41900), Succ(ywv39800)) → new_primMinusNat0(ywv41900, ywv39800)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch197(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3Size_r0(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch1150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_primMinusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1167(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, EmptyFM, x3, x4)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1183(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7, x8)
new_mkVBalBranch3MkVBalBranch1201(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_splitLT30(False, x0, x1, EmptyFM, x2, True, x3)
new_splitLT30(True, x0, x1, EmptyFM, x2, False, x3)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_primMulNat(Succ(x0))
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12, x13)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch1199(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch1142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch1143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch8(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch1137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C1(Branch(True, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1188(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch30(x0, x1, x2, Neg(Zero), x3, x4, x5, x6, Neg(Zero), x7, x8, x9)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch1151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch1156(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_addToFM00(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch191(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_mkVBalBranch3MkVBalBranch1180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch1101(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Zero), x9)
new_mkVBalBranch3MkVBalBranch1192(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13)
new_mkVBalBranch3MkVBalBranch1146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch1200(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch192(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1101(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Zero), x9)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1128(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch190(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch1190(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1116(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_sizeFM(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch1178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkVBalBranch3MkVBalBranch1108(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12)
new_mkVBalBranch3MkVBalBranch1123(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1102(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1201(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch1179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch1155(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch1102(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1201(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_splitLT30(False, x0, x1, Branch(x2, x3, x4, x5, x6), Branch(x7, x8, x9, x10, x11), True, x12)
new_mkVBalBranch3MkVBalBranch1116(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, Branch(x5, x6, x7, x8, x9), x10, x11, x12, x13)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1202(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1200(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch1160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_primMulNat(Zero)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch1195(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkVBalBranch10(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch1203(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch234(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch9(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Zero), x7, x8), x9)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch187(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_mkVBalBranch3MkVBalBranch1163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch1185(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_mkVBalBranch30(x0, x1, x2, Neg(Zero), x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10)
new_mkVBalBranch30(x0, x1, x2, Pos(Zero), x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkVBalBranch3MkVBalBranch1204(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT30(True, x0, x1, x2, x3, True, x4)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch1180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_mkVBalBranch3MkVBalBranch1200(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch183(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch9(x0, EmptyFM, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch1157(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch30(x0, x1, x2, Pos(Succ(x3)), x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1179(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_primPlusNat2(x0, Zero)
new_mkVBalBranch3MkVBalBranch1148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch1158(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1104(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1185(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch1194(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1201(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1102(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Zero), x9)
new_mkVBalBranch3MkVBalBranch1118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_splitGT(Branch(x0, x1, x2, x3, x4), x5)
new_mkVBalBranch3MkVBalBranch184(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Succ(x9)), x10)
new_splitLT30(False, x0, x1, x2, x3, False, x4)
new_mkVBalBranch3MkVBalBranch1188(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch1108(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13)
new_mkVBalBranch3MkVBalBranch1166(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, EmptyFM, x5, x6, x7, x8)
new_mkVBalBranch3MkVBalBranch1188(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_splitLT(Branch(x0, x1, x2, x3, x4), x5)
new_mkVBalBranch3MkVBalBranch1148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1100(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1194(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Zero), x3, x4), Branch(x5, x6, Pos(Succ(x7)), x8, x9), x10)
new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Neg(Succ(x7)), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, Zero, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch1101(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch1146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch1202(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_splitLT4(x0)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch1142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_addToFM_C2(Branch(False, x0, x1, x2, x3), x4, x5)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch188(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkVBalBranch3MkVBalBranch1136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkVBalBranch3MkVBalBranch1197(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch1140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, x4, x5)
new_primMulNat1(x0)
new_mkVBalBranch3MkVBalBranch1187(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch30(x0, x1, x2, Neg(Succ(x3)), x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch185(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primMulNat0(x0)
new_addToFM_C2(EmptyFM, x0, x1)
new_primMinusNat0(Succ(x0), Succ(x1))
new_mkVBalBranch3MkVBalBranch198(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch1171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12)
new_primPlusNat2(x0, Succ(x1))
new_mkVBalBranch3MkVBalBranch1148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkVBalBranch3MkVBalBranch1186(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_splitGT30(False, x0, x1, x2, Branch(x3, x4, x5, x6, x7), True, x8)
new_mkVBalBranch3MkVBalBranch1178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1189(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch1151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1154(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1105(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1122(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch1178(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch192(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_mkVBalBranch3MkVBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13)
new_mkVBalBranch3MkVBalBranch1164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1199(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch10(x0, Branch(x1, x2, x3, x4, x5), x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1196(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1120(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch1172(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch198(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch219(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch1203(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch1183(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch184(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Zero), x9)
new_mkVBalBranch3MkVBalBranch1160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch1101(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch1106(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch1152(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_primPlusNat3(Zero, Zero)
new_mkVBalBranch3MkVBalBranch1133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1109(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1103(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1192(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1120(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkVBalBranch3MkVBalBranch1136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch1132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_primPlusNat1(Succ(x0))
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitGT30(False, x0, x1, x2, x3, False, x4)
new_mkVBalBranch3MkVBalBranch1151(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch1141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch184(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Zero), x9)
new_mkVBalBranch3MkVBalBranch1176(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch1193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch1135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1191(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch1168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1168(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Zero, x4, x5, x6)
new_addToFM(x0, x1, x2)
new_mkVBalBranch3MkVBalBranch1150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch1135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch410(x0, x1, EmptyFM, x2, x3, x4)
new_mkVBalBranch3MkVBalBranch1160(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, x5, x6, x7)
new_primPlusNat1(Zero)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch1180(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1175(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_addToFM_C1(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Neg(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch1181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1194(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11)
new_addToFM_C1(Branch(False, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch1188(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Zero, x10)
new_mkVBalBranch3MkVBalBranch1127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch191(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1169(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1185(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch1153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch187(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1117(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch3MkVBalBranch1191(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch230(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch1193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Pos(x7), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch199(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Zero), x9)
new_mkVBalBranch3MkVBalBranch1184(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_primPlusNat3(Succ(x0), Succ(x1))
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Pos(Zero), x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1197(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch1170(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1171(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12, x13)
new_mkVBalBranch3MkVBalBranch1165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch1153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_primPlusInt(Neg(x0), Neg(x1))
new_mkVBalBranch3MkVBalBranch1143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitLT30(True, x0, x1, Branch(x2, x3, x4, x5, x6), x7, False, x8)
new_mkVBalBranch3MkVBalBranch187(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1120(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch1182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch1181(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_mkVBalBranch3MkVBalBranch199(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Succ(x9)), x10)
new_mkVBalBranch3MkVBalBranch1136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1161(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch1184(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch7(x0, EmptyFM, x1, x2)
new_mkVBalBranch3MkVBalBranch1194(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch1139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch1177(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1153(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Succ(x10)), x11)
new_mkVBalBranch3MkVBalBranch1200(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch196(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1189(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch1125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Zero), x10)
new_mkVBalBranch3MkVBalBranch1120(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_primPlusInt(Pos(x0), Neg(x1))
new_primPlusInt(Neg(x0), Pos(x1))
new_mkVBalBranch3MkVBalBranch1121(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch199(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Zero), x9)
new_mkVBalBranch3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1174(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_primMulNat2(Succ(x0))
new_mkVBalBranch3MkVBalBranch1119(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Zero), x3, x4), Branch(x5, x6, Pos(Zero), x7, x8), x9)
new_mkVBalBranch7(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkVBalBranch3MkVBalBranch189(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch192(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkBalBranch6MkBalBranch37(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch1198(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch1162(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkVBalBranch3MkVBalBranch1140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch1197(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_splitLT30(True, x0, x1, x2, x3, True, x4)
new_mkVBalBranch3MkVBalBranch1133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch30(x0, x1, x2, Pos(Zero), x3, x4, x5, x6, Pos(Zero), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1197(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch8(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch1136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Pos(Zero), x10)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch1147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(x11), x12)
new_mkVBalBranch3MkVBalBranch1204(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, Neg(Zero), x7, x8, x9, Succ(x10), x11)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1100(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch1198(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch1131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_splitGT30(False, x0, x1, x2, EmptyFM, True, x3)
new_mkVBalBranch30(x0, x1, x2, Pos(Zero), x3, x4, x5, x6, Pos(Succ(x7)), x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1193(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch1165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Pos(Zero), x11)
new_mkVBalBranch3MkVBalBranch186(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1163(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch7(x0, Branch(x1, x2, Pos(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11, x12)
new_mkVBalBranch3MkVBalBranch1165(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_emptyFM(x0)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch30(x0, x1, x2, Pos(Zero), x3, x4, x5, x6, Neg(Zero), x7, x8, x9)
new_mkVBalBranch30(x0, x1, x2, Neg(Zero), x3, x4, x5, x6, Pos(Zero), x7, x8, x9)
new_mkVBalBranch3MkVBalBranch1164(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(x12), x13)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_primPlusNat3(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch184(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Succ(x9)), x10)
new_splitLT(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch1107(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch1125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Neg(Succ(x10)), x11)
new_primPlusInt(Pos(x0), Pos(x1))
new_mkVBalBranch30(x0, x1, x2, Neg(Zero), x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch182(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch235(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch5(x0, EmptyFM, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch1130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch194(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1204(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Zero, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch199(x0, x1, x2, x3, x4, x5, x6, x7, x8, Neg(Succ(x9)), x10)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch195(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Zero), x11)
new_mkVBalBranch3MkVBalBranch1173(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(x11), x12)
new_mkVBalBranch3MkVBalBranch1195(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch1129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat2(Zero)
new_mkVBalBranch7(x0, Branch(x1, x2, Neg(Succ(x3)), x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C2(Branch(True, x0, x1, x2, x3), x4, x5)
new_mkVBalBranch3MkVBalBranch1204(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), Zero, x11)
new_mkVBalBranch3MkVBalBranch1203(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Neg(Succ(x11)), x12)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_mkVBalBranch3MkVBalBranch1159(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch1102(x0, x1, x2, x3, x4, x5, x6, x7, x8, Pos(Zero), x9)
new_splitLT30(False, x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, True, x7)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch187(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_addToFM0(x0, x1, x2, x3, x4, x5, x6)
new_primPlusNat3(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT(EmptyFM, x0)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, Neg(Succ(x7)), x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch1106(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(x12), x13)
new_mkVBalBranch3MkVBalBranch1103(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, Succ(x10), x11)
new_mkVBalBranch3MkVBalBranch1149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch6(x0, x1, x2, x3, x4, x5, EmptyFM, x6)
new_splitGT30(True, x0, x1, x2, x3, False, x4)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)

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: