YES 150.40200000000002 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 Int a  ->  FiniteMap Int b  ->  FiniteMap Int a) :: FiniteMap Int a  ->  FiniteMap Int b  ->  FiniteMap Int 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 (\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 a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt _ fm_l EmptyFM) = fm_l
deleteMax (Branch key elt _ fm_l fm_r) = mkBalBranch key elt fm_l (deleteMax fm_r)

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

  emptyFM :: FiniteMap b a
emptyFM = EmptyFM

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

  findMin :: FiniteMap 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_elt1) ->mid_elt1) vv2
mid_elt2 = (\(_,mid_elt2) ->mid_elt2) vv3
mid_key1 = (\(mid_key1,_) ->mid_key1) vv2
mid_key2 = (\(mid_key2,_) ->mid_key2) vv3
vv2 = findMax fm1
vv3 = findMin fm2

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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


module Maybe where
  import qualified FiniteMap
import qualified Prelude


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 Int b  ->  FiniteMap Int a  ->  FiniteMap Int b) :: FiniteMap Int b  ->  FiniteMap Int a  ->  FiniteMap Int b)

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

  
addToFM0 old new = new

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

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

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

  emptyFM :: FiniteMap a b
emptyFM = EmptyFM

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

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

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

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

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

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

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

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

  sIZE_RATIO :: Int
sIZE_RATIO = 5

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

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

  splitLT :: Ord 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


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

  
addToFM0 old new = new

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

  deleteMax :: Ord a => FiniteMap a b  ->  FiniteMap a b
deleteMax (Branch key elt 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 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 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 c => FiniteMap c a  ->  FiniteMap c b  ->  FiniteMap c a
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 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 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 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 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 b => b  ->  a  ->  FiniteMap b a  ->  FiniteMap b a  ->  FiniteMap b a
mkVBalBranch key elt EmptyFM fm_r = addToFM fm_r key elt
mkVBalBranch key elt fm_l EmptyFM = addToFM fm_l key elt
mkVBalBranch key elt (Branch 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 b => FiniteMap b a  ->  b  ->  FiniteMap b a
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 :: b  ->  a  ->  FiniteMap b a
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

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)

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

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

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)

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

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)

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

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

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_C1 combiner key elt size fm_l fm_r new_key new_elt True = mkBalBranch key elt fm_l (addToFM_C combiner fm_r new_key new_elt)
addToFM_C1 combiner key elt size fm_l fm_r new_key new_elt False = addToFM_C0 combiner key elt size fm_l fm_r new_key new_elt otherwise

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

addToFM_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

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 Int a  ->  FiniteMap Int b  ->  FiniteMap Int a) :: FiniteMap Int a  ->  FiniteMap Int b  ->  FiniteMap Int a)

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

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)

mkBalBranch6Size_l xwu xwv xww xwx = sizeFM xww

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)

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

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)

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

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)

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

mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xwx

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)

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)

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)

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

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)

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

mkBranchRight_ok xyy xyz xzu = mkBranchRight_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_size xyy xyz xzu = sizeFM xzu

mkBranchUnbox xyy xyz xzu x = x

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

mkBranchRight_size xyy xyz xzu = sizeFM xyy

mkBranchBalance_ok xyy xyz xzu = True

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)) xzy xzx

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
glueBal2Mid_elt20 xzz yuu (vyz,mid_elt2) = mid_elt2

glueBal2Vv2 xzz yuu = findMax xzz

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

glueBal2Mid_key20 xzz yuu (mid_key2,vzv) = mid_key2

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

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

glueBal2Mid_key10 xzz yuu (mid_key1,vzu) = mid_key1

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_elt2 xzz yuu = glueBal2Mid_elt20 xzz yuu (glueBal2Vv3 xzz yuu)

glueBal2Mid_elt10 xzz yuu (vyy,mid_elt1) = mid_elt1

glueBal2Vv3 xzz yuu = findMin yuu

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

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

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

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)

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

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

  
glueBal2GlueBal0 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 xzz

  
glueBal2Vv3 xzz yuu = findMin yuu

  
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 a  ->  FiniteMap c b  ->  FiniteMap c a
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_L fm_R key elt fm_L fm_R (mkBalBranch6Size_l key elt fm_L fm_R + mkBalBranch6Size_r key elt fm_L fm_R < 2)

  
mkBalBranch6Double_L 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 xww

  
mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xwx

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

  
mkBranchBalance_ok xyy xyz xzu = True

  
mkBranchLeft_ok xyy xyz xzu = mkBranchLeft_ok0 xyy xyz xzu xzu xyz 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_ok0Biggest_left_key ywu = fst (findMax ywu)

  
mkBranchLeft_size xyy xyz xzu = sizeFM xzu

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

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

  
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 xyy

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

  
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 yvu yvv yvw yvx yvy)

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

  
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


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 Int b  ->  FiniteMap Int a  ->  FiniteMap Int 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 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 b a
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 fm1 fm2 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 xzz

  
glueBal2Vv3 xzz yuu = findMin yuu

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

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

  
mkBalBranch6Size_r xwu xwv xww xwx = sizeFM xwx

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

  
mkBranchBalance_ok xyy xyz xzu = True

  
mkBranchLeft_ok xyy xyz xzu = mkBranchLeft_ok0 xyy xyz xzu xzu xyz 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_ok0Biggest_left_key ywu = fst (findMax ywu)

  
mkBranchLeft_size xyy xyz xzu = sizeFM xzu

  
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)) xzy xzx

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

  
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 xyy

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

  
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 yvu yvv yvw yvx yvy)

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

  
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 b a  ->  Int
sizeFM EmptyFM = Pos Zero
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 (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

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

new_glueBal2Mid_key10(ywv2905, ywv2906, ywv2907, ywv2908, ywv2909, ywv2910, ywv2911, ywv2912, ywv2913, ywv2914, ywv2915, ywv2916, ywv2917, ywv2918, Branch(ywv29190, ywv29191, ywv29192, ywv29193, ywv29194), h, ba) → new_glueBal2Mid_key10(ywv2905, ywv2906, ywv2907, ywv2908, ywv2909, ywv2910, ywv2911, ywv2912, ywv2913, ywv2914, ywv29190, ywv29191, ywv29192, ywv29193, ywv29194, 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

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

new_glueBal2Mid_elt10(ywv2889, ywv2890, ywv2891, ywv2892, ywv2893, ywv2894, ywv2895, ywv2896, ywv2897, ywv2898, ywv2899, ywv2900, ywv2901, ywv2902, Branch(ywv29030, ywv29031, ywv29032, ywv29033, ywv29034), h, ba) → new_glueBal2Mid_elt10(ywv2889, ywv2890, ywv2891, ywv2892, ywv2893, ywv2894, ywv2895, ywv2896, ywv2897, ywv2898, ywv29030, ywv29031, ywv29032, ywv29033, ywv29034, 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

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

new_glueBal2Mid_key20(ywv2873, ywv2874, ywv2875, ywv2876, ywv2877, ywv2878, ywv2879, ywv2880, ywv2881, ywv2882, ywv2883, ywv2884, ywv2885, Branch(ywv28860, ywv28861, ywv28862, ywv28863, ywv28864), ywv2887, h, ba) → new_glueBal2Mid_key20(ywv2873, ywv2874, ywv2875, ywv2876, ywv2877, ywv2878, ywv2879, ywv2880, ywv2881, ywv2882, ywv28860, ywv28861, ywv28862, ywv28863, ywv28864, 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

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

new_glueBal2Mid_elt20(ywv2857, ywv2858, ywv2859, ywv2860, ywv2861, ywv2862, ywv2863, ywv2864, ywv2865, ywv2866, ywv2867, ywv2868, ywv2869, Branch(ywv28700, ywv28701, ywv28702, ywv28703, ywv28704), ywv2871, h, ba) → new_glueBal2Mid_elt20(ywv2857, ywv2858, ywv2859, ywv2860, ywv2861, ywv2862, ywv2863, ywv2864, ywv2865, ywv2866, ywv28700, ywv28701, ywv28702, ywv28703, ywv28704, 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

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

new_primMinusNat(Succ(ywv132000), Succ(ywv542000)) → new_primMinusNat(ywv132000, ywv542000)

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

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

new_primPlusNat(Succ(ywv3540), Succ(ywv62000000)) → new_primPlusNat(ywv3540, ywv62000000)

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

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

new_mkBalBranch6MkBalBranch11(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv2954000), Succ(ywv295600), h, ba) → new_mkBalBranch6MkBalBranch11(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv2954000, ywv295600, 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
                                ↳ 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(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2930000), Succ(ywv293400), h, ba) → new_mkBalBranch6MkBalBranch3(ywv254330, ywv254331, ywv2851, ywv254334, ywv2930000, ywv293400, 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

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

new_mkBalBranch6MkBalBranch01(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv2932000), Succ(ywv295000), h, ba) → new_mkBalBranch6MkBalBranch01(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv2932000, ywv295000, 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

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

new_mkBalBranch6MkBalBranch4(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2921000), Succ(ywv292200), h, ba) → new_mkBalBranch6MkBalBranch4(ywv254330, ywv254331, ywv2851, ywv254334, ywv2921000, ywv292200, 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

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

new_deleteMax(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), h, ba) → new_deleteMax(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, 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

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

new_deleteMin(ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, h, ba) → new_deleteMin(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, 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

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

new_glueBal2GlueBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv2837000), Succ(ywv2836000), h, ba) → new_glueBal2GlueBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2837000, ywv2836000, 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
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27940, h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv275400, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, Zero, h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv275400, ywv27940, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Succ(Succ(ywv2697000)), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv275400), ywv27940, h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv275400, ywv27940, h, ba)
new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal16(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv275400, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Neg(ywv26970), h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27310, h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv269700, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal16(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(Succ(ywv2754000)), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, Succ(ywv27310), Pos(ywv26970), h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Succ(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv279300)), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv269700), ywv27310, h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, ywv27310, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Pos(ywv27540), h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2754, h, ba) → new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2754, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, ywv27310, h, ba)
new_glueVBal3GlueVBal16(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv279300), Succ(Succ(ywv2754000)), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(Succ(ywv2697000)), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv279300), Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2697, h, ba) → new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2697, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv27300, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat(Zero) → Zero
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat(Succ(ywv252500)) → new_primPlusNat0(new_primMulNat0(ywv252500), Succ(ywv252500))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv254330, ywv254331, ywv254332, ywv254333, ywv254334), h, ba)
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044), h, ba)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bb, bc) → ywv21132

The set Q consists of the following terms:

new_primMulNat1(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Succ(x1))
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat0(x0)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Zero)

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

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

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

new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27940, h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv275400, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Neg(ywv26970), h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27310, h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv269700, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, Succ(ywv27310), Pos(ywv26970), h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv279300)), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv275400, ywv27940, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Pos(ywv27540), h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, ywv27310, h, ba)
new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2754, h, ba) → new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2754, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv279300), Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2697, h, ba) → new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2697, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv27300, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primMulNat(Zero) → Zero
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat(Succ(ywv252500)) → new_primPlusNat0(new_primMulNat0(ywv252500), Succ(ywv252500))
new_sizeFM(EmptyFM, bb, bc) → Pos(Zero)
new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv254330, ywv254331, ywv254332, ywv254333, ywv254334), h, ba)
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044), h, ba)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bb, bc) → ywv21132

The set Q consists of the following terms:

new_primMulNat1(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Succ(x1))
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat0(x0)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Zero)

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

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

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

new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Zero), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Zero, h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27940, h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Succ(ywv2697000))), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv273000), Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv273000, ywv2697000, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal15(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv275400, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv273000)), Pos(Succ(Zero)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Zero), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Neg(ywv26970), h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)
new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv27310, h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal26(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, ywv269700, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, Zero, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Zero), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, Branch(ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334), ywv254334, Succ(ywv27310), Pos(ywv26970), h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Neg(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Neg(Zero), h, ba) → new_glueVBal3GlueVBal25(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(Succ(ywv279300)), Pos(Succ(Succ(ywv2754000))), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Neg(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv275400, ywv27940, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, Branch(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444), ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27940), Pos(ywv27540), h, ba) → new_glueVBal3(ywv250440, ywv250441, ywv250442, ywv250443, ywv250444, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal21(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27310), Neg(Succ(ywv269700)), h, ba) → new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv269700, ywv27310, h, ba)
new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2754, h, ba) → new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2754, h, ba)
new_glueVBal3GlueVBal22(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Succ(ywv2697000), h, ba) → new_glueVBal3GlueVBal24(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv27300), Pos(Zero), h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Succ(ywv279300), Succ(ywv2754000), h, ba) → new_glueVBal3GlueVBal13(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv279300, ywv2754000, h, ba)
new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv2697, h, ba) → new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), ywv2697, h, ba)
new_glueVBal3GlueVBal12(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Succ(ywv275400)), h, ba) → new_glueVBal3GlueVBal14(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Zero, Pos(Zero), h, ba) → new_glueVBal3GlueVBal27(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal2(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27030), ywv2697, h, ba) → new_glueVBal3GlueVBal20(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27030), ywv2697, h, ba)
new_glueVBal3(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba) → new_glueVBal3GlueVBal29(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv2543330, ywv2543331, ywv2543332, ywv2543333, ywv2543334, h, ba), h, ba)
new_glueVBal3GlueVBal28(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, ywv27300, Zero, h, ba) → new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba)
new_glueVBal3GlueVBal10(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, Pos(ywv27770), ywv2754, h, ba) → new_glueVBal3GlueVBal11(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_primMulNat(ywv27770), ywv2754, h, ba)
new_glueVBal3GlueVBal23(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_glueVBal3GlueVBal1(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba), h, ba)

The TRS R consists of the following rules:

new_primMulNat(Zero) → Zero
new_primMulNat(Succ(ywv252500)) → new_primPlusNat0(new_primMulNat0(ywv252500), Succ(ywv252500))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_glueVBal3Size_r(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv254330, ywv254331, ywv254332, ywv254333, ywv254334), h, ba)
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bb, bc) → ywv21132
new_glueVBal3Size_l(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044, ywv254330, ywv254331, ywv254332, ywv254333, ywv254334, h, ba) → new_sizeFM(Branch(ywv25040, ywv25041, ywv25042, ywv25043, ywv25044), h, ba)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_glueVBal3Size_r(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primMulNat(Succ(x0))
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Succ(x1))
new_sizeFM(EmptyFM, x0, x1)
new_primMulNat0(x0)
new_glueVBal3Size_l(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primMulNat(Zero)

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

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



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

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

new_addToFM_C(Branch(Pos(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_addToFM_C(ywv123, Zero, ywv31, h)
new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Zero, bb) → new_addToFM_C(ywv1837, Succ(ywv1838), ywv1839, bb)
new_addToFM_C(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_addToFM_C(ywv124, Zero, ywv31, h)
new_addToFM_C20(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ba) → new_addToFM_C1(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv1222), Succ(ywv1227), ba)
new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Succ(ywv18410), bb) → new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, ywv18400, ywv18410, bb)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Zero, ba) → new_addToFM_C1(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv1222), Succ(ywv1227), ba)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Zero, ba) → new_addToFM_C20(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ba)
new_addToFM_C(Branch(Neg(Zero), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C(ywv123, Succ(ywv3000), ywv31, h)
new_addToFM_C(Branch(Pos(ywv1200), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C(ywv123, Succ(ywv3000), ywv31, h)
new_addToFM_C(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C2(ywv12000, ywv121, ywv122, ywv123, ywv124, ywv3000, ywv31, ywv12000, ywv3000, h)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Succ(ywv12300), ba) → new_addToFM_C(ywv1225, Succ(ywv1227), ywv1228, ba)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Succ(ywv12300), ba) → new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ywv12290, ywv12300, ba)

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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Zero, bb) → new_addToFM_C(ywv1837, Succ(ywv1838), ywv1839, bb)
new_addToFM_C20(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ba) → new_addToFM_C1(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv1222), Succ(ywv1227), ba)
new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Succ(ywv18410), bb) → new_addToFM_C1(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, ywv18400, ywv18410, bb)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Zero, ba) → new_addToFM_C1(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv1222), Succ(ywv1227), ba)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Zero, ba) → new_addToFM_C20(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ba)
new_addToFM_C(Branch(Neg(Zero), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C(ywv123, Succ(ywv3000), ywv31, h)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Succ(ywv12300), ba) → new_addToFM_C(ywv1225, Succ(ywv1227), ywv1228, ba)
new_addToFM_C(Branch(Pos(ywv1200), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C(ywv123, Succ(ywv3000), ywv31, h)
new_addToFM_C(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C2(ywv12000, ywv121, ywv122, ywv123, ywv124, ywv3000, ywv31, ywv12000, ywv3000, h)
new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Succ(ywv12300), ba) → new_addToFM_C2(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ywv12290, ywv12300, 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
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C(Branch(Pos(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_addToFM_C(ywv123, Zero, ywv31, h)
new_addToFM_C(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_addToFM_C(ywv124, Zero, 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
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(ywv2660), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Succ(ywv18550), bd) → new_mkVBalBranch(ywv1852, ywv1853, ywv1848, ywv1849, Pos(Succ(Zero)), ywv1850, ywv1851, ywv1846, bd)
new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Neg(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, ywv1120, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(ywv319), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Zero)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv21500), bg) → new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(Succ(ywv1311)), bc)
new_mkVBalBranch3MkVBalBranch16(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, be) → new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), be)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Succ(ywv27910), Succ(ywv27920), h) → new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ywv27910, ywv27920, h)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Succ(ywv2177000))), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Zero, be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Zero, Succ(Zero), be)
new_mkVBalBranch3MkVBalBranch29(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Succ(ywv20550), bg) → new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv20540, ywv20550, bg)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv20550), bg) → new_mkVBalBranch(ywv2052, ywv2053, ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051, ywv2045, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, bg) → new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, ywv2660, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), Succ(Succ(ywv1311)), bc)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(ywv2610), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, ywv2610, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(ywv13170), bc) → new_mkVBalBranch(ywv1314, ywv1315, ywv1309, ywv1310, Pos(Succ(Succ(ywv1311))), ywv1312, ywv1313, ywv1307, bc)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch(ywv269, ywv270, ywv264, ywv265, Pos(Succ(Zero)), ywv267, ywv268, ywv262, bb)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, Succ(ywv266), bb)
new_mkVBalBranch3MkVBalBranch210(ywv259, ywv260, ywv261000, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch(ywv269, ywv270, ywv264, ywv265, Pos(Succ(Zero)), ywv267, ywv268, ywv262, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Zero, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Zero, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Succ(ywv7080), ba) → new_mkVBalBranch0(ywv300, ywv31, ywv334, ywv110, ywv111, ywv11200, ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Zero, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Neg(Zero), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Pos(Succ(ywv217800)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Succ(ywv27100), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), Succ(Zero), be)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch24(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch24(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv2177000), Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch24(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf) → new_mkVBalBranch3MkVBalBranch28(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(Succ(new_primPlusNat0(ywv27100, ywv2660))), ywv261000, bb)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Zero, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Zero, bd) → new_mkVBalBranch3MkVBalBranch28(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Succ(ywv13170), bc) → new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, ywv13160, ywv13170, bc)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Succ(ywv11200), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch3MkVBalBranch212(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv11200, Succ(ywv704), ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv7740), bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, Branch(ywv27880, ywv27881, ywv27882, ywv27883, ywv27884), ywv2789, ywv2790, Zero, Succ(ywv27920), h) → new_mkVBalBranch3(ywv2789, ywv2790, ywv27880, ywv27881, ywv27882, ywv27883, ywv27884, ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783, h)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Pos(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Succ(ywv18550), bd) → new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, ywv18540, ywv18550, bd)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch28(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, be) → new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), be)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Pos(ywv21770), bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv300, ywv31, Succ(ywv7030), ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch17(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, be) → new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), be)
new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), Succ(ywv266), bb)
new_mkVBalBranch0(ywv300, ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv110, ywv111, ywv11200, ywv113, ywv114, ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Succ(ywv26100)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Succ(ywv26100), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_sizeFM(EmptyFM, bh, ca) → Pos(Zero)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bh, ca) → ywv21132

The set Q consists of the following terms:

new_primMulNat1(x0)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

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

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

new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Succ(ywv18550), bd) → new_mkVBalBranch(ywv1852, ywv1853, ywv1848, ywv1849, Pos(Succ(Zero)), ywv1850, ywv1851, ywv1846, bd)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(ywv2660), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Neg(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, ywv1120, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(ywv319), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Zero)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv21500), bg) → new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(Succ(ywv1311)), bc)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Succ(ywv2177000))), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Succ(ywv27910), Succ(ywv27920), h) → new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ywv27910, ywv27920, h)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Zero, be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Zero, Succ(Zero), be)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Succ(ywv20550), bg) → new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv20540, ywv20550, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, bg) → new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv20550), bg) → new_mkVBalBranch(ywv2052, ywv2053, ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051, ywv2045, bg)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, ywv2660, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), Succ(Succ(ywv1311)), bc)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(ywv2610), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, ywv2610, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(ywv13170), bc) → new_mkVBalBranch(ywv1314, ywv1315, ywv1309, ywv1310, Pos(Succ(Succ(ywv1311))), ywv1312, ywv1313, ywv1307, bc)
new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch(ywv269, ywv270, ywv264, ywv265, Pos(Succ(Zero)), ywv267, ywv268, ywv262, bb)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, Succ(ywv266), bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Zero, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Zero, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Succ(ywv7080), ba) → new_mkVBalBranch0(ywv300, ywv31, ywv334, ywv110, ywv111, ywv11200, ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Zero, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Neg(Zero), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Pos(Succ(ywv217800)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Succ(ywv27100), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), Succ(Zero), be)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch24(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch24(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv2177000), Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch24(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf) → new_mkVBalBranch3MkVBalBranch28(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(Succ(new_primPlusNat0(ywv27100, ywv2660))), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Zero, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Zero, bd) → new_mkVBalBranch3MkVBalBranch28(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Succ(ywv11200), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch3MkVBalBranch212(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv11200, Succ(ywv704), ba)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Succ(ywv13170), bc) → new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, ywv13160, ywv13170, bc)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv7740), bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, Branch(ywv27880, ywv27881, ywv27882, ywv27883, ywv27884), ywv2789, ywv2790, Zero, Succ(ywv27920), h) → new_mkVBalBranch3(ywv2789, ywv2790, ywv27880, ywv27881, ywv27882, ywv27883, ywv27884, ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783, h)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Pos(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Succ(ywv18550), bd) → new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, ywv18540, ywv18550, bd)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch28(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, be) → new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), be)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Pos(ywv21770), bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv300, ywv31, Succ(ywv7030), ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch0(ywv300, ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv110, ywv111, ywv11200, ywv113, ywv114, ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), Succ(ywv266), bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Succ(ywv26100)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Succ(ywv26100), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_sizeFM(EmptyFM, bh, ca) → Pos(Zero)
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bh, ca) → ywv21132

The set Q consists of the following terms:

new_primMulNat1(x0)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ QDP
                                    ↳ UsableRulesProof
                                      ↳ QDP
                                        ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Succ(ywv18550), bd) → new_mkVBalBranch(ywv1852, ywv1853, ywv1848, ywv1849, Pos(Succ(Zero)), ywv1850, ywv1851, ywv1846, bd)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(ywv2660), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Neg(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, ywv1120, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(ywv319), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Zero)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv21500), bg) → new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(Succ(ywv1311)), bc)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv215000), Neg(Succ(Succ(ywv2177000))), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Succ(ywv27910), Succ(ywv27920), h) → new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ywv27910, ywv27920, h)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Zero, be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Zero, Succ(Zero), be)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Succ(ywv20550), bg) → new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv20540, ywv20550, bg)
new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, bg) → new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bg), bg)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv20550), bg) → new_mkVBalBranch(ywv2052, ywv2053, ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051, ywv2045, bg)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, ywv2660, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch27(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bc)
new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), bc) → new_mkVBalBranch3MkVBalBranch1(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), Succ(Succ(ywv1311)), bc)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(ywv2610), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, ywv2610, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(ywv13170), bc) → new_mkVBalBranch(ywv1314, ywv1315, ywv1309, ywv1310, Pos(Succ(Succ(ywv1311))), ywv1312, ywv1313, ywv1307, bc)
new_mkVBalBranch3MkVBalBranch18(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch(ywv269, ywv270, ywv264, ywv265, Pos(Succ(Zero)), ywv267, ywv268, ywv262, bb)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, Succ(ywv266), bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Zero, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Zero, bg) → new_mkVBalBranch3MkVBalBranch19(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bg)
new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Succ(ywv7080), ba) → new_mkVBalBranch0(ywv300, ywv31, ywv334, ywv110, ywv111, ywv11200, ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Zero), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Zero, ywv261000, bb)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Neg(Zero), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch212(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch213(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch111(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Pos(Succ(ywv217800)), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch22(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Succ(ywv27100), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), be) → new_mkVBalBranch3MkVBalBranch1(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), Succ(Zero), be)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Zero, bd) → new_mkVBalBranch3MkVBalBranch24(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch24(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv2177000), Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bg)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch24(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf) → new_mkVBalBranch3MkVBalBranch28(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, bf)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), bb) → new_mkVBalBranch3MkVBalBranch21(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(Succ(new_primPlusNat0(ywv27100, ywv2660))), ywv261000, bb)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Zero, bc) → new_mkVBalBranch3MkVBalBranch14(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bc)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Zero, bd) → new_mkVBalBranch3MkVBalBranch28(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, bd)
new_mkVBalBranch3MkVBalBranch211(ywv110, ywv111, Succ(ywv11200), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, ba) → new_mkVBalBranch3MkVBalBranch212(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv11200, Succ(ywv704), ba)
new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Succ(ywv13170), bc) → new_mkVBalBranch3MkVBalBranch21(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, ywv13160, ywv13170, bc)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch11(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), ba)
new_mkVBalBranch3MkVBalBranch23(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), bb)
new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv7740), bb) → new_mkVBalBranch0(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, bb)
new_mkVBalBranch3MkVBalBranch1(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, Branch(ywv27880, ywv27881, ywv27882, ywv27883, ywv27884), ywv2789, ywv2790, Zero, Succ(ywv27920), h) → new_mkVBalBranch3(ywv2789, ywv2790, ywv27880, ywv27881, ywv27882, ywv27883, ywv27884, ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783, h)
new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, Pos(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, Branch(ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114), ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Succ(ywv18550), bd) → new_mkVBalBranch3MkVBalBranch22(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, ywv18540, ywv18550, bd)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch20(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), ba)
new_mkVBalBranch3MkVBalBranch112(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv215000), bg) → new_mkVBalBranch3MkVBalBranch113(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bg)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, bb) → new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb)
new_mkVBalBranch3MkVBalBranch28(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, be) → new_mkVBalBranch3MkVBalBranch15(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), be)
new_mkVBalBranch3MkVBalBranch110(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Pos(ywv21770), bg) → new_mkVBalBranch0(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bg)
new_mkVBalBranch3MkVBalBranch10(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv300, ywv31, Succ(ywv7030), ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch25(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv269, ywv270, bb) → new_mkVBalBranch3(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, bb)
new_mkVBalBranch0(ywv300, ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv110, ywv111, ywv11200, ywv113, ywv114, ba) → new_mkVBalBranch3(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ba)
new_mkVBalBranch3MkVBalBranch12(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), bb) → new_mkVBalBranch3MkVBalBranch1(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), Succ(ywv266), bb)
new_mkVBalBranch3MkVBalBranch2(ywv259, ywv260, Neg(Succ(ywv26100)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, ba) → new_mkVBalBranch(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, ba)
new_mkVBalBranch3(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, ba) → new_mkVBalBranch3MkVBalBranch2(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), ba)
new_mkVBalBranch3MkVBalBranch26(ywv259, ywv260, Succ(ywv26100), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, bb) → new_mkVBalBranch3MkVBalBranch13(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), bb)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), bh, ca) → ywv21132

The set Q consists of the following terms:

new_primMulNat1(x0)
new_sizeFM(EmptyFM, x0, x1)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                              ↳ QDP
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C0(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C21(ywv34000, ywv341, ywv342, ywv343, ywv344, ywv3000, ywv31, ywv3000, ywv34000, bb)
new_addToFM_C0(Branch(Neg(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, bb) → new_addToFM_C0(ywv344, Zero, ywv31, bb)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Succ(ywv12180), h) → new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ywv12170, ywv12180, h)
new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Zero, ba) → new_addToFM_C0(ywv1826, Succ(ywv1827), ywv1828, ba)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Zero, h) → new_addToFM_C22(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, h)
new_addToFM_C0(Branch(Pos(Zero), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C0(ywv344, Succ(ywv3000), ywv31, bb)
new_addToFM_C0(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, bb) → new_addToFM_C0(ywv343, Zero, ywv31, bb)
new_addToFM_C22(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, h) → new_addToFM_C10(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv1215), Succ(ywv1210), h)
new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Succ(ywv18300), ba) → new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, ywv18290, ywv18300, ba)
new_addToFM_C0(Branch(Neg(ywv3400), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C0(ywv344, Succ(ywv3000), ywv31, bb)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Zero, h) → new_addToFM_C10(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv1215), Succ(ywv1210), h)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Succ(ywv12180), h) → new_addToFM_C0(ywv1213, Succ(ywv1215), ywv1216, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C0(Branch(Neg(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, bb) → new_addToFM_C0(ywv344, Zero, ywv31, bb)
new_addToFM_C0(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, bb) → new_addToFM_C0(ywv343, Zero, ywv31, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_addToFM_C0(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C21(ywv34000, ywv341, ywv342, ywv343, ywv344, ywv3000, ywv31, ywv3000, ywv34000, bb)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Succ(ywv12180), h) → new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ywv12170, ywv12180, h)
new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Zero, ba) → new_addToFM_C0(ywv1826, Succ(ywv1827), ywv1828, ba)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Zero, h) → new_addToFM_C22(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, h)
new_addToFM_C0(Branch(Pos(Zero), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C0(ywv344, Succ(ywv3000), ywv31, bb)
new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Succ(ywv18300), ba) → new_addToFM_C10(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, ywv18290, ywv18300, ba)
new_addToFM_C22(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, h) → new_addToFM_C10(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv1215), Succ(ywv1210), h)
new_addToFM_C0(Branch(Neg(ywv3400), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, bb) → new_addToFM_C0(ywv344, Succ(ywv3000), ywv31, bb)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Zero, h) → new_addToFM_C10(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv1215), Succ(ywv1210), h)
new_addToFM_C21(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Succ(ywv12180), h) → new_addToFM_C0(ywv1213, Succ(ywv1215), ywv1216, 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

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Zero, bc)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
The approximation of the Dependency Graph [15,17,22] contains 5 SCCs 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [12,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)



↳ 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
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), bc) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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_primMulNat2(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primMulNat0(ywv1952), Succ(ywv1952)), bc) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

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

new_primMulNat0(x0)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ 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
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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_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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1952), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv34200), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1952, ywv1952))), Succ(ywv1952)), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv34200, ywv34200))), Succ(ywv34200)), Succ(ywv34200)), Succ(ywv34200)), h) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952))), Succ(ywv1952)), Succ(ywv1952)), bc) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h) at position [11,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200))), Succ(ywv34200)), Succ(ywv34200)), h) at position [12,0] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952))), Succ(ywv1952)), bc) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)



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

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [11] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200))), Succ(ywv34200)), h) at position [12] we obtained the following new rules:

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch119(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), bd) → new_mkVBalBranch1(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), bd)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch118(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv34200, ywv34200)), ywv34200)), ywv34200)), ywv34200))), h)
new_mkVBalBranch3MkVBalBranch117(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = x1 + x2 + x3 + x5   
POL(Neg(x1)) = 1 + x1   
POL(Pos(x1)) = 1 + x1   
POL(Succ(x1)) = 0   
POL(Zero) = 1   
POL(new_mkVBalBranch1(x1, x2, x3, x4, x5)) = x3   
POL(new_mkVBalBranch3MkVBalBranch116(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = x10   
POL(new_mkVBalBranch3MkVBalBranch117(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x9   
POL(new_mkVBalBranch3MkVBalBranch118(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x7 + x9   
POL(new_mkVBalBranch3MkVBalBranch120(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7   
POL(new_mkVBalBranch3MkVBalBranch121(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10   
POL(new_mkVBalBranch3MkVBalBranch217(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x10 + x6 + x7   
POL(new_mkVBalBranch3MkVBalBranch218(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x10 + x6 + x7   
POL(new_mkVBalBranch3MkVBalBranch219(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x10 + x6 + x7   
POL(new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, bc) → new_mkVBalBranch3MkVBalBranch219(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, bc)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, bc) → new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1952, ywv1952)), ywv1952)), ywv1952)), ywv1952))), bc)
new_mkVBalBranch3MkVBalBranch120(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), bc) → new_mkVBalBranch3MkVBalBranch121(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), bc)
new_mkVBalBranch3MkVBalBranch116(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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 5 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                      ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                      ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)

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

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ UsableRulesProof
                                                                                                                                                                                                                                          ↳ QDP
                                                                                                                                                                                                                                            ↳ QReductionProof
                                                                                                                                                                                                                                              ↳ QDP
                                                                                                                                                                                                                                                ↳ QDPSizeChangeProof
                                                                                                                                                                                                                                      ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), bd) → new_mkVBalBranch3MkVBalBranch121(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, bd)

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

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



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ 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
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ Rewriting
                                                ↳ QDP
                                                  ↳ Rewriting
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ UsableRulesProof
                                                            ↳ QDP
                                                              ↳ QReductionProof
                                                                ↳ QDP
                                                                  ↳ Rewriting
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ Rewriting
                                                                                ↳ QDP
                                                                                  ↳ Rewriting
                                                                                    ↳ QDP
                                                                                      ↳ UsableRulesProof
                                                                                        ↳ QDP
                                                                                          ↳ QReductionProof
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ UsableRulesProof
                                                                                                                ↳ QDP
                                                                                                                  ↳ QReductionProof
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ Rewriting
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ Rewriting
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ Rewriting
                                                                                                                                        ↳ QDP
                                                                                                                                          ↳ Rewriting
                                                                                                                                            ↳ QDP
                                                                                                                                              ↳ Rewriting
                                                                                                                                                ↳ QDP
                                                                                                                                                  ↳ Rewriting
                                                                                                                                                    ↳ QDP
                                                                                                                                                      ↳ Rewriting
                                                                                                                                                        ↳ QDP
                                                                                                                                                          ↳ Rewriting
                                                                                                                                                            ↳ QDP
                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                ↳ QDP
                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                    ↳ QDP
                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                        ↳ QDP
                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                            ↳ QDP
                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                          ↳ Rewriting
                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                              ↳ Rewriting
                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                  ↳ Rewriting
                                                                                                                                                                                                                    ↳ QDP
                                                                                                                                                                                                                      ↳ Rewriting
                                                                                                                                                                                                                        ↳ QDP
                                                                                                                                                                                                                          ↳ DependencyGraphProof
                                                                                                                                                                                                                            ↳ QDP
                                                                                                                                                                                                                              ↳ QDPOrderProof
                                                                                                                                                                                                                                ↳ QDP
                                                                                                                                                                                                                                  ↳ DependencyGraphProof
                                                                                                                                                                                                                                    ↳ AND
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                      ↳ QDP
                                                                                                                                                                                                                                        ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), bc) → new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, bc)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch218(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), bc) → new_mkVBalBranch1(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, bc)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h)
new_mkVBalBranch3MkVBalBranch217(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch218(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)

The TRS R consists of the following rules:

new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h)

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

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                            ↳ QDP
                                              ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), 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
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), ywv343, h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), ywv343, h)

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

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ 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_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), ywv343, h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), ywv343, h)

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

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ UsableRulesProof
                                        ↳ QDP
                                          ↳ QReductionProof
                                            ↳ QDP
                                              ↳ QDPSizeChangeProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primMulNat2(x0)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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_primMulNat2(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primMulNat0(ywv1937), Succ(ywv1937)), ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))
new_primMulNat0(x0)

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

new_primMulNat0(x0)



↳ HASKELL
  ↳ LR
    ↳ HASKELL
      ↳ CR
        ↳ HASKELL
          ↳ BR
            ↳ HASKELL
              ↳ COR
                ↳ HASKELL
                  ↳ 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
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primMulNat1(x0)
new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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_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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Zero, Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(ywv1937), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(ywv1937, ywv1937))), Succ(ywv1937)), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937))), Succ(ywv1937)), Succ(ywv1937)), ba) at position [12,0] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(Succ(x0), Succ(x1))

We have to consider all minimal (P,Q,R)-chains.
By rewriting [15] the rule new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primPlusNat0(Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937))), Succ(ywv1937)), ba) at position [12] we obtained the following new rules:

new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ QDPOrderProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), ba) → new_mkVBalBranch1(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, ba)
The remaining pairs can at least be oriented weakly.

new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
Used ordering: Polynomial interpretation [25]:

POL(Branch(x1, x2, x3, x4, x5)) = 1 + x1 + x4   
POL(Pos(x1)) = 0   
POL(Succ(x1)) = 0   
POL(Zero) = 0   
POL(new_mkVBalBranch1(x1, x2, x3, x4, x5)) = x4   
POL(new_mkVBalBranch3MkVBalBranch114(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x4   
POL(new_mkVBalBranch3MkVBalBranch115(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x1 + x4   
POL(new_mkVBalBranch3MkVBalBranch214(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)) = 1 + x1 + x4   
POL(new_mkVBalBranch3MkVBalBranch215(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)) = 1 + x1 + x4   
POL(new_mkVBalBranch3MkVBalBranch216(x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)) = 1 + x1 + x4   
POL(new_primPlusNat0(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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ Rewriting
                                        ↳ QDP
                                          ↳ Rewriting
                                            ↳ QDP
                                              ↳ UsableRulesProof
                                                ↳ QDP
                                                  ↳ QReductionProof
                                                    ↳ QDP
                                                      ↳ Rewriting
                                                        ↳ QDP
                                                          ↳ Rewriting
                                                            ↳ QDP
                                                              ↳ UsableRulesProof
                                                                ↳ QDP
                                                                  ↳ QReductionProof
                                                                    ↳ QDP
                                                                      ↳ Rewriting
                                                                        ↳ QDP
                                                                          ↳ Rewriting
                                                                            ↳ QDP
                                                                              ↳ UsableRulesProof
                                                                                ↳ QDP
                                                                                  ↳ QReductionProof
                                                                                    ↳ QDP
                                                                                      ↳ Rewriting
                                                                                        ↳ QDP
                                                                                          ↳ Rewriting
                                                                                            ↳ QDP
                                                                                              ↳ Rewriting
                                                                                                ↳ QDP
                                                                                                  ↳ Rewriting
                                                                                                    ↳ QDP
                                                                                                      ↳ Rewriting
                                                                                                        ↳ QDP
                                                                                                          ↳ Rewriting
                                                                                                            ↳ QDP
                                                                                                              ↳ Rewriting
                                                                                                                ↳ QDP
                                                                                                                  ↳ Rewriting
                                                                                                                    ↳ QDP
                                                                                                                      ↳ Rewriting
                                                                                                                        ↳ QDP
                                                                                                                          ↳ Rewriting
                                                                                                                            ↳ QDP
                                                                                                                              ↳ DependencyGraphProof
                                                                                                                                ↳ QDP
                                                                                                                                  ↳ QDPOrderProof
                                                                                                                                    ↳ QDP
                                                                                                                                      ↳ QDPSizeChangeProof
                              ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bb) → new_mkVBalBranch1(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bb)
new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), ba) → new_mkVBalBranch3MkVBalBranch115(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), ba)
new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bb) → new_mkVBalBranch3MkVBalBranch115(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bb)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch1(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, ba) → new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)
new_mkVBalBranch1(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), ba) → new_mkVBalBranch3MkVBalBranch215(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, ba)
new_mkVBalBranch3MkVBalBranch214(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch215(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_mkVBalBranch3MkVBalBranch216(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ba) → new_mkVBalBranch3MkVBalBranch114(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv1937, ywv1937)), ywv1937)), ywv1937)), ywv1937))), ba)

The TRS R consists of the following rules:

new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_primPlusNat0(Zero, Zero) → Zero
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)

The set Q consists of the following terms:

new_primPlusNat0(Zero, Succ(x0))
new_primPlusNat0(Zero, Zero)
new_primPlusNat0(Succ(x0), Zero)
new_primPlusNat0(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
                                ↳ DependencyGraphProof
                              ↳ QDP
                              ↳ QDP

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

new_splitLT3(Pos(Zero), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT20(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, ba)
new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), ba) → new_splitLT2(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, ba)
new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Zero, bd) → new_splitLT4(ywv657, ywv658, bd)
new_splitLT3(Pos(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), ba)
new_splitLT22(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, bc) → new_splitLT10(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv238), Succ(ywv243), bc)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Succ(ywv2360), bb) → new_splitLT(ywv232, ywv234, bb)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Zero, bb) → new_splitLT21(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, bb)
new_splitLT3(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT4(ywv33, ywv4000, ba)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Zero, bc) → new_splitLT22(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, bc)
new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Zero, h) → new_splitLT(ywv632, ywv633, h)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Succ(ywv2450), bc) → new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ywv2440, ywv2450, bc)
new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Succ(ywv6600), bd) → new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ywv6590, ywv6600, bd)
new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), ba) → new_splitLT5(ywv34, ba)
new_splitLT4(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), ba)
new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Pos(Zero), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Pos(Zero), ba)
new_splitLT(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT0(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Pos(Zero), ba)
new_splitLT5(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Zero), ba)
new_splitLT3(Neg(ywv300), ywv31, ywv32, EmptyFM, ywv34, Pos(Succ(ywv4000)), ba) → new_splitLT(ywv34, ywv4000, ba)
new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Succ(ywv6350), h) → new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ywv6340, ywv6350, h)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Succ(ywv2450), bc) → new_splitLT4(ywv241, ywv243, bc)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Succ(ywv2360), bb) → new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, ywv2350, ywv2360, bb)
new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), ba) → new_splitLT0(ywv34, ba)
new_splitLT3(Neg(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Zero, bb) → new_splitLT1(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv234), Succ(ywv229), bb)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Zero, bc) → new_splitLT10(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv238), Succ(ywv243), bc)
new_splitLT21(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, bb) → new_splitLT1(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv234), Succ(ywv229), bb)
new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Zero), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Zero), ba)

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 4 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Pos(Zero), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Pos(Zero), ba)
new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), ba) → new_splitLT0(ywv34, ba)
new_splitLT0(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Pos(Zero), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), ba) → new_splitLT5(ywv34, ba)
new_splitLT5(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Zero), ba)
new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Zero), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Zero), 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                              ↳ QDP
                              ↳ QDP

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

new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Succ(ywv6600), bd) → new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ywv6590, ywv6600, bd)
new_splitLT4(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), ba)
new_splitLT3(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT4(ywv33, ywv4000, ba)
new_splitLT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT20(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, ba)
new_splitLT10(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Zero, bd) → new_splitLT4(ywv657, ywv658, bd)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Zero, bc) → new_splitLT22(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, bc)
new_splitLT3(Pos(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Succ(ywv4000)), ba) → new_splitLT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), ba)
new_splitLT22(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, bc) → new_splitLT10(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv238), Succ(ywv243), bc)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Succ(ywv2450), bc) → new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ywv2440, ywv2450, bc)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Zero, bc) → new_splitLT10(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv238), Succ(ywv243), bc)
new_splitLT20(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Succ(ywv2450), bc) → new_splitLT4(ywv241, ywv243, bc)

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

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



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

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

new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Succ(ywv2360), bb) → new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, ywv2350, ywv2360, bb)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Zero, bb) → new_splitLT21(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, bb)
new_splitLT3(Pos(Zero), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT3(Neg(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, ba) → new_splitLT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), ba)
new_splitLT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), ba) → new_splitLT2(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, ba)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Zero, bb) → new_splitLT1(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv234), Succ(ywv229), bb)
new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Zero, h) → new_splitLT(ywv632, ywv633, h)
new_splitLT2(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Succ(ywv2360), bb) → new_splitLT(ywv232, ywv234, bb)
new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Succ(ywv6350), h) → new_splitLT1(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ywv6340, ywv6350, h)
new_splitLT3(Neg(ywv300), ywv31, ywv32, EmptyFM, ywv34, Pos(Succ(ywv4000)), ba) → new_splitLT(ywv34, ywv4000, ba)
new_splitLT21(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, bb) → new_splitLT1(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv234), Succ(ywv229), 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

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

new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Zero, bc) → new_splitGT22(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bc)
new_splitGT1(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Zero, bc) → new_splitGT1(ywv224, ywv225, bc)
new_splitGT3(Pos(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Succ(ywv4000)), h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)
new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Neg(Zero), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Neg(Zero), h)
new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_splitGT0(ywv33, h)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Succ(ywv2270), bc) → new_splitGT11(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv220), Succ(ywv225), bc)
new_splitGT3(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT(ywv34, ywv4000, h)
new_splitGT21(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ba) → new_splitGT10(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv216), Succ(ywv211), ba)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Succ(ywv2180), ba) → new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ywv2170, ywv2180, ba)
new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitGT20(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, h)
new_splitGT3(Neg(ywv300), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Succ(ywv2180), ba) → new_splitGT10(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv216), Succ(ywv211), ba)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Zero, ba) → new_splitGT(ywv215, ywv216, ba)
new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Succ(ywv5880), Succ(ywv5890), bb) → new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, ywv5880, ywv5890, bb)
new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Zero, Succ(ywv6260), bd) → new_splitGT1(ywv622, ywv624, bd)
new_splitGT0(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Zero), h)
new_splitGT(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Succ(ywv2270), bc) → new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, ywv2260, ywv2270, bc)
new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Zero), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Zero), h)
new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_splitGT4(ywv33, h)
new_splitGT22(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bc) → new_splitGT11(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv220), Succ(ywv225), bc)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Zero, ba) → new_splitGT21(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ba)
new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Zero, Succ(ywv5890), bb) → new_splitGT(ywv585, ywv587, bb)
new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT2(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, h)
new_splitGT3(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitGT1(ywv33, ywv4000, h)
new_splitGT4(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Neg(Zero), h)
new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Succ(ywv6250), Succ(ywv6260), bd) → new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, ywv6250, ywv6260, bd)

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 4 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP

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

new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Succ(ywv5880), Succ(ywv5890), bb) → new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, ywv5880, ywv5890, bb)
new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT2(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, h)
new_splitGT3(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT(ywv34, ywv4000, h)
new_splitGT21(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ba) → new_splitGT10(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv216), Succ(ywv211), ba)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Zero, ba) → new_splitGT21(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ba)
new_splitGT10(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Zero, Succ(ywv5890), bb) → new_splitGT(ywv585, ywv587, bb)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Succ(ywv2180), ba) → new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ywv2170, ywv2180, ba)
new_splitGT(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Succ(ywv2180), ba) → new_splitGT10(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv216), Succ(ywv211), ba)
new_splitGT3(Neg(ywv300), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_splitGT2(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Zero, ba) → new_splitGT(ywv215, ywv216, 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
                                ↳ DependencyGraphProof
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                                    ↳ QDP
                              ↳ QDP

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

new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_splitGT0(ywv33, h)
new_splitGT0(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Zero), h)
new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Zero), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Zero), 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
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                                    ↳ QDP
                              ↳ QDP

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

new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Neg(Zero), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Neg(Zero), h)
new_splitGT3(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_splitGT4(ywv33, h)
new_splitGT4(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT3(ywv340, ywv341, ywv342, ywv343, ywv344, Neg(Zero), 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
                                  ↳ AND
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                    ↳ QDP
                                      ↳ QDPSizeChangeProof
                              ↳ QDP

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

new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Zero, bc) → new_splitGT22(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bc)
new_splitGT1(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Zero, bc) → new_splitGT1(ywv224, ywv225, bc)
new_splitGT3(Pos(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv34, Neg(Succ(ywv4000)), h) → new_splitGT3(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)
new_splitGT22(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bc) → new_splitGT11(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv220), Succ(ywv225), bc)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Succ(ywv2270), bc) → new_splitGT11(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv220), Succ(ywv225), bc)
new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Zero, Succ(ywv6260), bd) → new_splitGT1(ywv622, ywv624, bd)
new_splitGT3(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitGT1(ywv33, ywv4000, h)
new_splitGT3(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitGT20(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, h)
new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Succ(ywv6250), Succ(ywv6260), bd) → new_splitGT11(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, ywv6250, ywv6260, bd)
new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Succ(ywv2270), bc) → new_splitGT20(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, ywv2260, ywv2270, bc)

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

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



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

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_mkVBalBranch3MkVBalBranch140(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), de) → new_mkVBalBranch3MkVBalBranch127(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv20370), Succ(ywv1942), de)
new_splitLT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitLT23(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, h)
new_mkVBalBranch3MkVBalBranch125(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h) → new_mkBalBranch(ywv90, ywv91, ywv93, new_mkVBalBranch4(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Int, h)
new_mkVBalBranch3MkVBalBranch143(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Zero, dg) → new_mkVBalBranch3MkVBalBranch144(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, dg)
new_mkVBalBranch3MkVBalBranch136(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Succ(ywv7030), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch7(ywv300, ywv31, ywv334, ywv110, ywv111, ywv11200, ywv113, ywv114, h), ty_Int, h)
new_splitLT13(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Succ(ywv6350), ef) → new_splitLT13(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ywv6340, ywv6350, ef)
new_mkBalBranch(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, new_primPlusInt0(new_mkBalBranch6Size_l(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, Zero, bc, bd) → new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkBalBranch6MkBalBranch312(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29370), bc, bd) → new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_addToFM_C26(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Zero, ce) → new_addToFM_C23(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ce)
new_addToFM_C4(Branch(Neg(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, h) → new_mkBalBranch(Neg(Succ(ywv34000)), ywv341, ywv343, new_addToFM_C4(ywv344, Zero, ywv31, h), ty_Int, h)
new_mkBalBranch6Size_l(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_sizeFM(ywv2851, bc, bd)
new_mkBalBranch6MkBalBranch312(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch42(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), ty_Int, h)
new_mkBalBranch6MkBalBranch017(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, EmptyFM, ywv2543344, bc, bd) → error([])
new_mkVBalBranch3MkVBalBranch141(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ty_Int, h)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch220(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, ywv2660, ywv261000, cb)
new_splitLT25(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Zero, ec) → new_splitLT26(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ec)
new_addToFM_C4(Branch(Neg(ywv3400), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, h) → new_mkBalBranch(Neg(ywv3400), ywv341, ywv343, new_addToFM_C4(ywv344, Succ(ywv3000), ywv31, h), ty_Int, h)
new_splitGT8(EmptyFM, h) → new_emptyFM(h)
new_splitLT7(EmptyFM, ywv4000, h) → new_splitLT40(ywv4000, h)
new_splitGT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_mkVBalBranch5(ywv31, new_splitGT5(ywv33, ywv4000, h), ywv34, h)
new_addToFM_C3(Branch(Pos(Zero), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → Branch(Neg(Zero), new_addToFM0(ywv121, ywv31, h), ywv122, ywv123, ywv124)
new_mkVBalBranch3MkVBalBranch237(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Zero, de) → new_mkVBalBranch3MkVBalBranch238(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, de)
new_addToFM_C13(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Zero, Succ(ywv18410), eg) → new_addToFM_C14(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, eg)
new_mkBalBranch6MkBalBranch0110(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv29460), bc, bd) → new_mkBalBranch6MkBalBranch018(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Succ(ywv292100)), Neg(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch410(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, new_primMulNat(ywv29200), bc, bd)
new_mkVBalBranch3MkVBalBranch123(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, bf) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv2812), ywv2813, Branch(ywv2807, ywv2808, Pos(Succ(ywv2809)), ywv2810, ywv2811), Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), ty_Int, bf)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Pos(Zero), Pos(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch010(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_primMulNat3(ywv29330), bc, bd)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Zero), Neg(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch412(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29200), bc, bd)
new_mkVBalBranch3MkVBalBranch150(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, db) → new_mkVBalBranch3MkVBalBranch149(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, new_primMulNat2(ywv1321), db)
new_mkBalBranch6MkBalBranch119(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv29580), bc, bd) → new_mkBalBranch6MkBalBranch1115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, ywv29580, bc, bd)
new_mkVBalBranch3MkVBalBranch238(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, de) → new_mkVBalBranch3MkVBalBranch140(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, new_primMulNat2(ywv1937), de)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Succ(ywv293000)), Pos(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch311(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, new_primMulNat(ywv29310), bc, bd)
new_mkVBalBranch4(ywv300, ywv31, EmptyFM, ywv34, h) → new_addToFM2(ywv34, ywv300, ywv31, h)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Zero), Pos(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch38(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29310), bc, bd)
new_mkBalBranch6MkBalBranch411(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT25(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Zero, ec) → new_splitLT26(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ec)
new_primMulNat3(Zero) → Zero
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(Zero)), bc, bd) → new_mkBalBranch6MkBalBranch51(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h), ywv344, ty_Int, h)
new_mkVBalBranch3MkVBalBranch138(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Zero, Zero, ea) → new_mkVBalBranch3MkVBalBranch145(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ea)
new_mkVBalBranch3MkVBalBranch137(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), bg) → new_mkVBalBranch3MkVBalBranch138(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv14040), Succ(Succ(ywv1311)), bg)
new_mkBalBranch6MkBalBranch412(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29290), bc, bd) → new_mkBalBranch6MkBalBranch41(ywv254330, ywv254331, ywv2851, ywv254334, ywv29290, Zero, bc, bd)
new_mkBalBranch6MkBalBranch1113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_splitLT9(EmptyFM, h) → new_emptyFM(h)
new_splitGT6(EmptyFM, ywv4000, h) → new_emptyFM(h)
new_addToFM_C4(Branch(Pos(Zero), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, h) → new_mkBalBranch(Pos(Zero), ywv341, ywv343, new_addToFM_C4(ywv344, Succ(ywv3000), ywv31, h), ty_Int, h)
new_splitLT8(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), h) → new_splitLT30(ywv330, ywv331, ywv332, ywv333, ywv334, Pos(Zero), h)
new_splitGT13(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Succ(ywv6250), Succ(ywv6260), cc) → new_splitGT13(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, ywv6250, ywv6260, cc)
new_mkBalBranch6MkBalBranch119(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch231(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch235(ywv110, ywv111, Succ(ywv11200), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, h) → new_mkVBalBranch3MkVBalBranch232(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv11200, Succ(ywv704), h)
new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch116(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, Branch(ywv110, ywv111, ywv112, ywv113, ywv114), h) → new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, h)
new_splitGT24(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bh) → new_splitGT13(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv220), Succ(ywv225), bh)
new_mkVBalBranch8(ywv269, ywv270, EmptyFM, ywv259, ywv260, ywv262, ywv263, cb) → new_addToFM1(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv269, ywv270, cb)
new_splitLT23(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Succ(ywv2360), cg) → new_splitLT7(ywv232, ywv234, cg)
new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch30(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch40(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, h) → new_addToFM1(ywv330, ywv331, ywv332, ywv333, ywv334, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch220(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Succ(ywv13170), bg) → new_mkVBalBranch3MkVBalBranch220(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, ywv13160, ywv13170, bg)
new_mkBalBranch6MkBalBranch1112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv2961, bc, bd) → new_mkBalBranch6MkBalBranch1115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv2961, ywv295400, bc, bd)
new_mkVBalBranch3MkVBalBranch229(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, df) → new_mkVBalBranch3MkVBalBranch228(ywv1553, ywv1554, ywv1555, ywv1556, ywv1557, ywv1558, ywv1559, ywv1560, ywv1561, ywv1562, ywv1563, df)
new_mkVBalBranch5(ywv31, EmptyFM, ywv34, h) → new_addToFM_C3(ywv34, Zero, ywv31, h)
new_addToFM_C25(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Zero, cf) → new_addToFM_C24(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, cf)
new_mkVBalBranch3MkVBalBranch142(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6170), h) → new_mkBalBranch(ywv90, ywv91, ywv93, new_mkVBalBranch4(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Int, h)
new_splitGT13(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Zero, Succ(ywv6260), cc) → new_mkVBalBranch6(ywv619, ywv620, new_splitGT5(ywv622, ywv624, cc), ywv623, cc)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Zero), cb) → new_mkVBalBranch3MkVBalBranch227(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Zero, ywv261000, cb)
new_addToFM_C26(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv12170), Succ(ywv12180), ce) → new_addToFM_C26(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ywv12170, ywv12180, ce)
new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv2932000), Succ(ywv295000), bc, bd) → new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv2932000, ywv295000, bc, bd)
new_splitGT14(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Zero, Succ(ywv5890), dh) → new_mkVBalBranch4(Succ(ywv582), ywv583, new_splitGT6(ywv585, ywv587, dh), ywv586, dh)
new_mkBalBranch6MkBalBranch315(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29360), bc, bd) → new_mkBalBranch6MkBalBranch310(ywv254330, ywv254331, ywv2851, ywv254334, Zero, ywv29360, bc, bd)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Zero), Pos(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch411(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29200), bc, bd)
new_splitGT6(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, h) → new_splitGT30(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkBalBranch(ywv90, ywv91, ywv93, new_mkVBalBranch4(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h), ty_Int, h)
new_mkVBalBranch3MkVBalBranch146(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch147(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv215000), bb) → new_mkVBalBranch3MkVBalBranch131(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkVBalBranch3MkVBalBranch148(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch138(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, Succ(ywv266), cb)
new_mkBalBranch6MkBalBranch32(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, Zero, bc, bd) → new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Zero), ywv83, ywv84), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(ywv3000)), ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Zero), ywv83, ywv84), ty_Int, h)
new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2921000), Succ(ywv292200), bc, bd) → new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, ywv2921000, ywv292200, bc, bd)
new_mkBalBranch6MkBalBranch413(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch42(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch132(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb) → new_mkVBalBranch3MkVBalBranch122(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkBalBranch6MkBalBranch1114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_splitLT9(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), h) → new_splitLT30(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Zero), h)
new_primPlusInt(ywv22140, Pos(ywv22290)) → Pos(new_primPlusNat0(ywv22140, ywv22290))
new_addToFM_C26(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Zero, ce) → new_addToFM_C23(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ce)
new_mkVBalBranch3MkVBalBranch220(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Succ(ywv13160), Zero, bg) → new_mkVBalBranch3MkVBalBranch221(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bg)
new_mkVBalBranch3MkVBalBranch224(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, cd) → new_mkVBalBranch3MkVBalBranch128(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, new_primMulNat2(ywv1952), cd)
new_mkVBalBranch3MkVBalBranch138(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Succ(ywv27910), Succ(ywv27920), ea) → new_mkVBalBranch3MkVBalBranch138(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ywv27910, ywv27920, ea)
new_mkBalBranch6MkBalBranch010(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, bc, bd) → new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Neg(ywv2610), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), cb) → new_mkVBalBranch3MkVBalBranch240(ywv259, ywv260, ywv2610, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Pos(Zero), Neg(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch016(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_primMulNat3(ywv29330), bc, bd)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Pos(Zero), Pos(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch119(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, new_primMulNat3(ywv29550), bc, bd)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Neg(Succ(ywv293200)), Neg(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch011(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_primMulNat3(ywv29330), ywv293200, bc, bd)
new_mkVBalBranch3MkVBalBranch141(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Succ(ywv7080), h) → new_mkBalBranch(ywv330, ywv331, ywv333, new_mkVBalBranch7(ywv300, ywv31, ywv334, ywv110, ywv111, ywv11200, ywv113, ywv114, h), ty_Int, h)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Succ(ywv8200)), ywv83, ywv84), h) → new_mkBalBranch(ywv80, ywv81, new_mkVBalBranch2(Succ(ywv3000), ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv83, h), ywv84, ty_Int, h)
new_mkVBalBranch6(ywv3000, ywv31, EmptyFM, ywv8, h) → new_addToFM(ywv8, ywv3000, ywv31, h)
new_mkVBalBranch3MkVBalBranch223(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkVBalBranch3MkVBalBranch148(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primMulNat2(Zero), cb)
new_splitGT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_splitGT8(ywv34, h)
new_mkVBalBranch10(ywv269, ywv270, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv259, ywv260, ywv262, ywv263, cb) → new_mkVBalBranch30(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Neg(Zero), ywv262, ywv263, cb)
new_mkBalBranch6MkBalBranch111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, Zero, bc, bd) → new_mkBalBranch6MkBalBranch113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch1110(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv29590), bc, bd) → new_mkBalBranch6MkBalBranch113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch220(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(ywv13170), bg) → new_mkBalBranch(ywv1304, ywv1305, new_mkVBalBranch2(ywv1314, ywv1315, ywv1309, ywv1310, Pos(Succ(Succ(ywv1311))), ywv1312, ywv1313, ywv1307, bg), ywv1308, ty_Int, bg)
new_primPlusInt1(ywv22140, Pos(ywv22300)) → new_primMinusNat0(ywv22300, ywv22140)
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Zero), bc, bd) → new_mkBalBranch6MkBalBranch51(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Zero), cb) → new_mkVBalBranch3MkVBalBranch220(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(ywv2660), ywv261000, cb)
new_splitGT30(Pos(ywv300), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_mkVBalBranch4(ywv300, ywv31, new_splitGT5(ywv33, ywv4000, h), ywv34, h)
new_splitLT30(Neg(ywv300), ywv31, ywv32, EmptyFM, ywv34, Pos(Succ(ywv4000)), h) → new_addToFM_C3(new_splitLT7(ywv34, ywv4000, h), ywv300, ywv31, h)
new_addToFM_C3(EmptyFM, ywv300, ywv31, h) → Branch(Neg(ywv300), ywv31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch227(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Zero, da) → new_mkVBalBranch3MkVBalBranch228(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, da)
new_splitLT30(Pos(ywv300), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitLT6(ywv33, ywv4000, h)
new_mkVBalBranch3MkVBalBranch232(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Succ(ywv20550), bb) → new_mkVBalBranch3MkVBalBranch232(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv20540, ywv20550, bb)
new_mkBalBranch6MkBalBranch40(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv2922, bc, bd) → new_mkBalBranch6MkBalBranch41(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv2922, bc, bd)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), EmptyFM, h) → new_addToFM(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv3000, ywv31, h)
new_splitGT25(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Zero, eb) → new_splitGT26(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, eb)
new_primMulNat(Succ(ywv252500)) → new_primPlusNat0(new_primMulNat0(ywv252500), Succ(ywv252500))
new_mkVBalBranch3MkVBalBranch138(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Succ(ywv27910), Zero, ea) → new_mkVBalBranch3MkVBalBranch145(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ea)
new_splitLT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → ywv33
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, h) → new_mkVBalBranch3MkVBalBranch234(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), h)
new_mkBalBranch6MkBalBranch41(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, Succ(ywv29220), bc, bd) → new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv29220, bc, bd)
new_mkVBalBranch3MkVBalBranch143(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Succ(ywv28300), dg) → new_mkVBalBranch3MkVBalBranch143(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, ywv28290, ywv28300, dg)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), cb) → new_mkVBalBranch3MkVBalBranch220(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv2660, ywv267, ywv268, ywv269, ywv270, Succ(Succ(new_primPlusNat0(ywv27100, ywv2660))), ywv261000, cb)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch226(ywv259, ywv260, ywv261000, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, cb)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334), Branch(ywv80, ywv81, ywv82, ywv83, ywv84), h) → new_mkVBalBranch3MkVBalBranch239(ywv80, ywv81, ywv82, ywv83, ywv84, ywv330, ywv331, ywv33200, ywv333, ywv334, Succ(ywv3000), ywv31, new_primMulNat0(ywv33200), h)
new_addToFM_C4(Branch(Pos(Zero), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, h) → Branch(Pos(Zero), new_addToFM0(ywv341, ywv31, h), ywv342, ywv343, ywv344)
new_mkBalBranch6MkBalBranch42(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, new_mkBalBranch6Size_l(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), new_mkBalBranch6Size_r(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, Succ(ywv295000), bc, bd) → new_mkBalBranch6MkBalBranch018(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkBalBranch6MkBalBranch32(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, Succ(ywv29340), bc, bd) → new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv29340, bc, bd)
new_mkBalBranch6MkBalBranch0110(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, bc, bd) → new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitGT23(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Succ(ywv2270), bh) → new_splitGT24(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bh)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Zero), Pos(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch315(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29310), bc, bd)
new_addToFM_C26(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Zero, Succ(ywv12180), ce) → new_mkBalBranch(Pos(Succ(ywv1210)), ywv1211, new_addToFM_C4(ywv1213, Succ(ywv1215), ywv1216, ce), ywv1214, ty_Int, ce)
new_mkVBalBranch3MkVBalBranch124(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkVBalBranch3MkVBalBranch125(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_mkBalBranch6MkBalBranch48(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), ywv343, h), ywv344, ty_Int, h)
new_mkVBalBranch3MkVBalBranch231(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkVBalBranch3MkVBalBranch236(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv34200, Succ(ywv616), h)
new_splitLT24(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, cg) → new_splitLT13(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv234), Succ(ywv229), cg)
new_mkBalBranch6MkBalBranch111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, Succ(ywv29560), bc, bd) → new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv29560, bc, bd)
new_splitGT7(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT30(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Zero), h)
new_splitGT8(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_splitGT30(ywv340, ywv341, ywv342, ywv343, ywv344, Neg(Zero), h)
new_mkBalBranch6MkBalBranch5(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch414(ywv254330, ywv254331, ywv2851, ywv254334, new_mkBalBranch6Size_l(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch010(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv29420), bc, bd) → new_mkBalBranch6MkBalBranch011(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, ywv29420, bc, bd)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), ty_Int, h)
new_addToFM_C25(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv12290), Succ(ywv12300), cf) → new_addToFM_C25(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, ywv12290, ywv12300, cf)
new_splitLT23(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Zero, cg) → new_splitLT24(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, cg)
new_splitLT12(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Zero, ca) → new_mkVBalBranch6(ywv653, ywv654, ywv656, new_splitLT6(ywv657, ywv658, ca), ca)
new_addToFM_C3(Branch(Pos(ywv1200), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_mkBalBranch(Pos(ywv1200), ywv121, new_addToFM_C3(ywv123, Succ(ywv3000), ywv31, h), ywv124, ty_Int, h)
new_mkVBalBranch3MkVBalBranch147(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkBalBranch(ywv264, ywv265, ywv267, new_mkVBalBranch7(ywv269, ywv270, ywv268, ywv259, ywv260, ywv26100, ywv262, ywv263, cb), ty_Int, cb)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch233(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_addToFM0(ywv341, ywv31, h) → ywv31
new_mkVBalBranch3MkVBalBranch225(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb) → new_mkVBalBranch3MkVBalBranch133(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_primMulNat2(ywv2044), bb)
new_mkVBalBranch3MkVBalBranch127(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Succ(ywv28150), bf) → new_mkVBalBranch3MkVBalBranch127(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, ywv28140, ywv28150, bf)
new_splitGT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_splitGT7(ywv34, h)
new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, Zero, Zero, bc, bd) → new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBranch(ywv2796, ywv2797, ywv2798, ywv2799, ywv2800, dc, dd) → Branch(ywv2797, ywv2798, new_primPlusInt2(new_primPlusInt(Succ(Zero), new_sizeFM(ywv2799, dc, dd)), ywv2800, ywv2797, ywv2799, dc, dd), ywv2799, ywv2800)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), cb) → new_mkVBalBranch3MkVBalBranch222(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_addToFM_C12(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Succ(ywv18300), be) → new_addToFM_C12(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, ywv18290, ywv18300, be)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Pos(Succ(ywv293200)), Neg(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch015(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkBalBranch6Size_r(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_sizeFM(ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, EmptyFM, ywv254334, bc, bd) → error([])
new_splitLT26(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ec) → new_splitLT12(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv238), Succ(ywv243), ec)
new_splitLT11(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ca) → ywv656
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(ywv293000)), Neg(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch314(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, new_primMulNat(ywv29310), bc, bd)
new_addToFM_C25(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Succ(ywv12300), cf) → new_mkBalBranch(Neg(Succ(ywv1222)), ywv1223, new_addToFM_C3(ywv1225, Succ(ywv1227), ywv1228, cf), ywv1226, ty_Int, cf)
new_mkVBalBranch3MkVBalBranch148(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), cb) → new_mkVBalBranch3MkVBalBranch138(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv8120), Succ(ywv266), cb)
new_mkVBalBranch3MkVBalBranch220(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, Zero, bg) → new_mkVBalBranch3MkVBalBranch221(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bg)
new_mkVBalBranch3MkVBalBranch135(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch132(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkBalBranch6MkBalBranch113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch116(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Succ(ywv292100)), Pos(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch49(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, new_primMulNat(ywv29200), bc, bd)
new_mkBalBranch6MkBalBranch015(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd) → new_mkBalBranch6MkBalBranch017(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitGT13(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Zero, Zero, cc) → new_splitGT12(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, cc)
new_mkVBalBranch3MkVBalBranch138(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, Zero, Succ(ywv27920), ea) → new_mkBalBranch(ywv2784, ywv2785, ywv2787, new_mkVBalBranch9(ywv2789, ywv2790, ywv2788, ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ea), ty_Int, ea)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Pos(Zero), Neg(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch1110(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, new_primMulNat3(ywv29550), bc, bd)
new_mkVBalBranch3MkVBalBranch236(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Zero, cd) → new_mkVBalBranch3MkVBalBranch224(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, cd)
new_mkVBalBranch8(ywv269, ywv270, Branch(ywv2680, ywv2681, ywv2682, ywv2683, ywv2684), ywv259, ywv260, ywv262, ywv263, cb) → new_mkVBalBranch30(ywv269, ywv270, ywv2680, ywv2681, ywv2682, ywv2683, ywv2684, ywv259, ywv260, Pos(Zero), ywv262, ywv263, cb)
new_mkBalBranch6MkBalBranch43(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch237(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv19480), de) → new_mkBalBranch(ywv1935, ywv1936, new_mkVBalBranch4(ywv1945, ywv1946, Branch(ywv1940, ywv1941, Pos(Succ(ywv1942)), ywv1943, ywv1944), ywv1938, de), ywv1939, ty_Int, de)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, h) → new_mkBalBranch(ywv110, ywv111, new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv113, h), ywv114, ty_Int, h)
new_mkVBalBranch3MkVBalBranch236(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Zero, cd) → new_mkVBalBranch3MkVBalBranch224(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, cd)
new_primMulNat1(ywv5200) → new_primPlusNat0(Zero, Succ(ywv5200))
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch126(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_mkVBalBranch3MkVBalBranch236(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, Succ(ywv19630), cd) → new_mkBalBranch(ywv1950, ywv1951, new_mkVBalBranch4(ywv1960, ywv1961, Branch(ywv1955, ywv1956, Neg(Succ(ywv1957)), ywv1958, ywv1959), ywv1953, cd), ywv1954, ty_Int, cd)
new_splitLT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_splitLT8(ywv33, h)
new_primMinusNat0(Succ(ywv132000), Zero) → Pos(Succ(ywv132000))
new_sizeFM(EmptyFM, ed, ee) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch227(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Zero, da) → new_mkVBalBranch3MkVBalBranch229(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, da)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(ywv292100)), Neg(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch47(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, new_primMulNat(ywv29200), bc, bd)
new_mkBalBranch6MkBalBranch39(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv2939, bc, bd) → new_mkBalBranch6MkBalBranch310(ywv254330, ywv254331, ywv2851, ywv254334, ywv2939, ywv293000, bc, bd)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Succ(ywv8200)), ywv83, ywv84), h) → new_mkVBalBranch3MkVBalBranch141(ywv80, ywv81, ywv8200, ywv83, ywv84, ywv330, ywv331, ywv333, ywv334, Succ(ywv3000), ywv31, new_primMulNat2(ywv8200), h)
new_mkVBalBranch3MkVBalBranch149(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Zero, db) → new_mkVBalBranch3MkVBalBranch138(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Zero, Succ(Zero), db)
new_addToFM1(ywv330, ywv331, ywv332, ywv333, ywv334, ywv300, ywv31, h) → new_addToFM_C3(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv300, ywv31, h)
new_mkBalBranch6MkBalBranch011(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, ywv293200, bc, bd) → new_mkBalBranch6MkBalBranch018(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkVBalBranch3MkVBalBranch232(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch225(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_splitLT23(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Succ(ywv2350), Succ(ywv2360), cg) → new_splitLT23(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, ywv2350, ywv2360, cg)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Succ(ywv261000))), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Succ(Succ(ywv27100)), cb) → new_mkVBalBranch3MkVBalBranch227(ywv259, ywv260, Succ(ywv261000), ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, Succ(ywv27100), ywv261000, cb)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, ywv92, ywv93, ywv94), EmptyFM, h) → new_addToFM2(Branch(ywv90, ywv91, ywv92, ywv93, ywv94), ywv300, ywv31, h)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Zero), ywv83, ywv84), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(ywv3000)), ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Zero), ywv83, ywv84), ty_Int, h)
new_splitLT6(EmptyFM, ywv4000, h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch48(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29240), bc, bd) → new_mkBalBranch6MkBalBranch415(ywv254330, ywv254331, ywv2851, ywv254334, Zero, ywv29240, bc, bd)
new_addToFM_C24(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, cf) → new_addToFM_C13(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Succ(ywv1222), Succ(ywv1227), cf)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch124(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200)), h)
new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, EmptyFM, h) → new_mkVBalBranch40(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, h)
new_mkBalBranch6MkBalBranch415(ywv254330, ywv254331, ywv2851, ywv254334, Zero, ywv292100, bc, bd) → new_mkBalBranch6MkBalBranch413(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_addToFM_C13(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Zero, eg) → new_mkBalBranch(Neg(Succ(ywv1833)), ywv1834, ywv1836, new_addToFM_C3(ywv1837, Succ(ywv1838), ywv1839, eg), ty_Int, eg)
new_mkVBalBranch3MkVBalBranch140(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, de) → new_mkVBalBranch3MkVBalBranch127(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Zero, Succ(ywv1942), de)
new_splitGT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_mkVBalBranch4(Succ(ywv3000), ywv31, new_splitGT7(ywv33, h), ywv34, h)
new_mkBalBranch6MkBalBranch017(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, Branch(ywv25433430, ywv25433431, ywv25433432, ywv25433433, ywv25433434), ywv2543344, bc, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Zero)))), ywv25433430, ywv25433431, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Zero))))), ywv254330, ywv254331, ywv2851, ywv25433433, bc, bd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))), ywv2543340, ywv2543341, ywv25433434, ywv2543344, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch310(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29390), ywv293000, bc, bd) → new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, ywv29390, ywv293000, bc, bd)
new_mkVBalBranch5(ywv31, Branch(ywv100, ywv101, ywv102, ywv103, ywv104), EmptyFM, h) → new_mkVBalBranch40(Zero, ywv31, ywv100, ywv101, ywv102, ywv103, ywv104, h)
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Succ(ywv285300)), bc, bd) → new_mkBalBranch6MkBalBranch51(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT30(Neg(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), Pos(Succ(ywv4000)), h) → new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, new_splitLT30(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h), h)
new_primPlusNat0(Succ(ywv3540), Zero) → Succ(ywv3540)
new_primPlusNat0(Zero, Succ(ywv62000000)) → Succ(ywv62000000)
new_primPlusInt2(Pos(ywv28380), ywv2800, ywv2797, ywv2799, dc, dd) → new_primPlusInt(ywv28380, new_sizeFM(ywv2800, dc, dd))
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Zero), Neg(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch312(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29310), bc, bd)
new_splitGT7(EmptyFM, h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch1114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv29630), bc, bd) → new_mkBalBranch6MkBalBranch111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv29630, Zero, bc, bd)
new_mkVBalBranch7(ywv300, ywv31, EmptyFM, ywv110, ywv111, ywv11200, ywv113, ywv114, h) → new_addToFM1(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, ywv300, ywv31, h)
new_mkVBalBranch3MkVBalBranch134(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Neg(Succ(ywv217700)), bb) → new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv217700, ywv21500, bb)
new_splitLT12(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Succ(ywv6590), Succ(ywv6600), ca) → new_splitLT12(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ywv6590, ywv6600, ca)
new_splitLT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → ywv33
new_splitLT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → ywv33
new_mkBalBranch6MkBalBranch49(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv2926, bc, bd) → new_mkBalBranch6MkBalBranch413(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, Zero, bc, bd) → new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch412(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Neg(Zero), Neg(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch1114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, new_primMulNat3(ywv29550), bc, bd)
new_primMulNat(Zero) → Zero
new_splitLT25(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Zero, Succ(ywv2450), ec) → new_splitLT6(ywv241, ywv243, ec)
new_splitLT23(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, Zero, Zero, cg) → new_splitLT24(ywv229, ywv230, ywv231, ywv232, ywv233, ywv234, cg)
new_mkBalBranch6MkBalBranch51(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBranch(Zero, ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT40(ywv4000, h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch130(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb) → new_mkVBalBranch3MkVBalBranch122(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkVBalBranch3MkVBalBranch234(ywv110, ywv111, Pos(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, h) → new_mkBalBranch(ywv110, ywv111, new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, h), ywv114, ty_Int, h)
new_addToFM_C14(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, eg) → Branch(Neg(Succ(ywv1838)), new_addToFM0(ywv1834, ywv1839, eg), ywv1835, ywv1836, ywv1837)
new_addToFM_C4(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, h) → new_mkBalBranch(Pos(Succ(ywv34000)), ywv341, new_addToFM_C4(ywv343, Zero, ywv31, h), ywv344, ty_Int, h)
new_addToFM_C3(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_mkBalBranch(Neg(Succ(ywv12000)), ywv121, ywv123, new_addToFM_C3(ywv124, Zero, ywv31, h), ty_Int, h)
new_mkVBalBranch3MkVBalBranch135(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Pos(Zero), bb) → new_mkVBalBranch3MkVBalBranch132(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_primMulNat2(ywv34200) → new_primPlusNat0(new_primMulNat0(ywv34200), Succ(ywv34200))
new_mkVBalBranch3MkVBalBranch137(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, Zero, bg) → new_mkVBalBranch3MkVBalBranch138(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, Succ(ywv1311), ywv1312, ywv1313, ywv1314, ywv1315, Zero, Succ(Succ(ywv1311)), bg)
new_mkBalBranch6MkBalBranch410(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv2927, bc, bd) → new_mkBalBranch6MkBalBranch415(ywv254330, ywv254331, ywv2851, ywv254334, ywv2927, ywv292100, bc, bd)
new_addToFM_C13(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Succ(ywv18400), Succ(ywv18410), eg) → new_addToFM_C13(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, ywv18400, ywv18410, eg)
new_splitGT26(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, eb) → new_splitGT14(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv216), Succ(ywv211), eb)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Zero), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv2710), cb) → new_mkVBalBranch3MkVBalBranch233(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkBalBranch6MkBalBranch013(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv293200, Zero, bc, bd) → new_mkBalBranch6MkBalBranch015(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitGT14(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Succ(ywv5880), Succ(ywv5890), dh) → new_splitGT14(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, ywv5880, ywv5890, dh)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Zero), Pos(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch48(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29200), bc, bd)
new_primPlusInt1(ywv22140, Neg(ywv22300)) → Neg(new_primPlusNat0(ywv22140, ywv22300))
new_mkBalBranch6MkBalBranch116(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, EmptyFM, ywv254334, bc, bd) → error([])
new_splitGT5(EmptyFM, ywv4000, h) → new_emptyFM(h)
new_mkBalBranch6MkBalBranch35(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch30(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_addToFM(ywv8, ywv3000, ywv31, h) → new_addToFM_C3(ywv8, Succ(ywv3000), ywv31, h)
new_splitLT30(Neg(ywv300), ywv31, ywv32, Branch(ywv330, ywv331, ywv332, ywv333, ywv334), EmptyFM, Pos(Succ(ywv4000)), h) → new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, ywv332, ywv333, ywv334, new_splitLT40(ywv4000, h), h)
new_splitGT12(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, cc) → ywv623
new_mkBalBranch6MkBalBranch414(ywv254330, ywv254331, ywv2851, ywv254334, ywv2920, bc, bd) → new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, new_mkBalBranch6Size_r(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd), ywv2920, bc, bd)
new_mkVBalBranch3MkVBalBranch231(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv616, h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Succ(ywv9200)), ywv93, ywv94), ywv343, h), ywv344, ty_Int, h)
new_mkVBalBranch3MkVBalBranch144(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, dg) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv2827), ywv2828, Branch(ywv2822, ywv2823, Neg(Succ(ywv2824)), ywv2825, ywv2826), Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), ty_Int, dg)
new_primMulNat0(ywv5200) → new_primPlusNat0(new_primPlusNat0(new_primPlusNat0(new_primMulNat1(ywv5200), Succ(ywv5200)), Succ(ywv5200)), Succ(ywv5200))
new_mkBalBranch6MkBalBranch311(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv2938, bc, bd) → new_mkBalBranch6MkBalBranch35(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Zero), Neg(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch31(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29310), bc, bd)
new_mkBalBranch6MkBalBranch118(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv2957, bc, bd) → new_mkBalBranch6MkBalBranch113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch38(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch018(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd) → new_mkBranch(Succ(Succ(Zero)), ywv2543340, ywv2543341, new_mkBranch(Succ(Succ(Succ(Zero))), ywv254330, ywv254331, ywv2851, ywv2543343, bc, bd), ywv2543344, bc, bd)
new_mkBalBranch6MkBalBranch47(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, ywv2923, bc, bd) → new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT25(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, Succ(ywv2440), Succ(ywv2450), ec) → new_splitLT25(ywv238, ywv239, ywv240, ywv241, ywv242, ywv243, ywv2440, ywv2450, ec)
new_mkBalBranch6MkBalBranch43(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29250), bc, bd) → new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, Branch(ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344), bc, bd) → new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_sizeFM(ywv2543343, bc, bd), new_sizeFM(ywv2543344, bc, bd), bc, bd)
new_mkVBalBranch3MkVBalBranch133(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv21500), bb) → new_mkVBalBranch3MkVBalBranch134(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bb), bb)
new_splitLT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitLT6(ywv33, ywv4000, h)
new_mkBalBranch6MkBalBranch016(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, bc, bd) → new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Zero), ywv113, ywv114, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Neg(Zero), ywv113, ywv114), ty_Int, h)
new_splitLT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_mkVBalBranch4(Zero, ywv31, ywv33, new_splitLT7(ywv34, ywv4000, h), h)
new_splitLT13(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Zero, Zero, ef) → new_splitLT14(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ef)
new_splitGT23(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Zero, Zero, bh) → new_splitGT24(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, bh)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Neg(Zero), Neg(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch0111(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_primMulNat3(ywv29330), bc, bd)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch222(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, Succ(ywv2660), ywv267, ywv268, ywv269, ywv270, cb)
new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, EmptyFM, bc, bd) → error([])
new_mkVBalBranch3MkVBalBranch227(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Zero, Succ(ywv18550), da) → new_mkBalBranch(ywv1843, ywv1844, new_mkVBalBranch2(ywv1852, ywv1853, ywv1848, ywv1849, Pos(Succ(Zero)), ywv1850, ywv1851, ywv1846, da), ywv1847, ty_Int, da)
new_addToFM_C23(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, ce) → new_addToFM_C12(ywv1210, ywv1211, ywv1212, ywv1213, ywv1214, ywv1215, ywv1216, Succ(ywv1215), Succ(ywv1210), ce)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Neg(Succ(ywv295400)), Neg(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch1112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, new_primMulNat3(ywv29550), bc, bd)
new_primPlusInt2(Neg(ywv28380), ywv2800, ywv2797, ywv2799, dc, dd) → new_primPlusInt1(ywv28380, new_sizeFM(ywv2800, dc, dd))
new_mkVBalBranch3MkVBalBranch133(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, bb) → new_mkVBalBranch3MkVBalBranch135(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, new_sizeFM(Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), ty_Int, bb), bb)
new_addToFM_C12(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Zero, Zero, be) → new_addToFM_C11(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, be)
new_addToFM_C3(Branch(Neg(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_addToFM_C25(ywv12000, ywv121, ywv122, ywv123, ywv124, ywv3000, ywv31, ywv12000, ywv3000, h)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Neg(ywv2610), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch240(ywv259, ywv260, ywv2610, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2921000), Zero, bc, bd) → new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_primPlusNat0(Zero, Zero) → Zero
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Succ(ywv9200)), ywv93, ywv94), Branch(ywv340, ywv341, Pos(ywv3420), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch230(ywv340, ywv341, ywv3420, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv9200, ywv9200)), ywv9200)), ywv9200)), ywv9200), h)
new_mkVBalBranch3MkVBalBranch149(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), db) → new_mkVBalBranch3MkVBalBranch138(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, Zero, ywv1326, ywv1327, ywv1328, ywv1329, Succ(ywv14050), Succ(Zero), db)
new_splitGT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → ywv34
new_splitGT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → ywv34
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h) → new_mkVBalBranch3MkVBalBranch142(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, new_primMulNat2(ywv34200), h)
new_splitLT12(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Zero, Zero, ca) → new_splitLT11(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ca)
new_splitGT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT6(ywv34, ywv4000, h)
new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, Zero, Succ(ywv292200), bc, bd) → new_mkBalBranch6MkBalBranch413(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, h) → new_mkVBalBranch3MkVBalBranch136(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), h)
new_mkVBalBranch3MkVBalBranch239(ywv259, ywv260, Pos(Succ(Zero)), ywv262, ywv263, ywv264, ywv265, Zero, ywv267, ywv268, ywv269, ywv270, Zero, cb) → new_mkVBalBranch3MkVBalBranch229(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, cb)
new_addToFM_C3(Branch(Neg(Zero), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → Branch(Neg(Zero), new_addToFM0(ywv121, ywv31, h), ywv122, ywv123, ywv124)
new_mkVBalBranch3MkVBalBranch127(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Zero, bf) → new_mkVBalBranch3MkVBalBranch123(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, bf)
new_mkVBalBranch10(ywv269, ywv270, EmptyFM, ywv259, ywv260, ywv262, ywv263, cb) → new_addToFM1(ywv259, ywv260, Neg(Zero), ywv262, ywv263, ywv269, ywv270, cb)
new_splitGT5(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, h) → new_splitGT30(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)
new_addToFM2(ywv34, ywv300, ywv31, h) → new_addToFM_C4(ywv34, ywv300, ywv31, h)
new_splitGT25(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Zero, Succ(ywv2180), eb) → new_splitGT26(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, eb)
new_mkVBalBranch3MkVBalBranch139(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, db) → new_mkVBalBranch3MkVBalBranch150(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, db)
new_sizeFM(Branch(ywv21130, ywv21131, ywv21132, ywv21133, ywv21134), ed, ee) → ywv21132
new_mkVBalBranch9(ywv2789, ywv2790, EmptyFM, ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ea) → new_addToFM1(ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783, ywv2789, ywv2790, ea)
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(Succ(Succ(ywv28530000)))), bc, bd) → new_mkBalBranch6MkBalBranch5(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_addToFM_C3(Branch(Pos(Succ(ywv12000)), ywv121, ywv122, ywv123, ywv124), Zero, ywv31, h) → new_mkBalBranch(Pos(Succ(ywv12000)), ywv121, new_addToFM_C3(ywv123, Zero, ywv31, h), ywv124, ty_Int, h)
new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, Succ(ywv295600), bc, bd) → new_mkBalBranch6MkBalBranch114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_addToFM_C3(Branch(Neg(Zero), ywv121, ywv122, ywv123, ywv124), Succ(ywv3000), ywv31, h) → new_mkBalBranch(Neg(Zero), ywv121, new_addToFM_C3(ywv123, Succ(ywv3000), ywv31, h), ywv124, ty_Int, h)
new_mkVBalBranch3MkVBalBranch124(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv12190), h) → new_mkVBalBranch3MkVBalBranch125(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, h)
new_addToFM_C12(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Zero, Succ(ywv18300), be) → new_addToFM_C11(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, be)
new_mkBalBranch6MkBalBranch114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))), ywv28510, ywv28511, ywv28513, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))), ywv254330, ywv254331, ywv28514, ywv254334, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv2954000), Succ(ywv295600), bc, bd) → new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv2954000, ywv295600, bc, bd)
new_splitLT12(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, Zero, Succ(ywv6600), ca) → new_splitLT11(ywv653, ywv654, ywv655, ywv656, ywv657, ywv658, ca)
new_mkVBalBranch3MkVBalBranch126(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), ty_Int, h)
new_primMinusNat0(Zero, Zero) → Pos(Zero)
new_mkVBalBranch3MkVBalBranch232(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv20540), Zero, bb) → new_mkVBalBranch3MkVBalBranch225(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_addToFM_C13(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, Zero, Zero, eg) → new_addToFM_C14(ywv1833, ywv1834, ywv1835, ywv1836, ywv1837, ywv1838, ywv1839, eg)
new_mkVBalBranch3MkVBalBranch234(ywv110, ywv111, Neg(ywv1120), ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv319, h) → new_mkVBalBranch3MkVBalBranch235(ywv110, ywv111, ywv1120, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primPlusNat0(Succ(ywv319), ywv33200), h)
new_mkBalBranch6MkBalBranch1111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv2960, bc, bd) → new_mkBalBranch6MkBalBranch114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Neg(Succ(ywv293000)), Neg(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch39(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, new_primMulNat(ywv29310), bc, bd)
new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv2932000), Zero, bc, bd) → new_mkBalBranch6MkBalBranch015(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitGT25(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Zero, eb) → new_splitGT6(ywv215, ywv216, eb)
new_mkBalBranch6MkBalBranch313(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv2934, bc, bd) → new_mkBalBranch6MkBalBranch32(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv2934, bc, bd)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Neg(Succ(ywv293200)), Pos(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch018(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitGT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitGT23(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, h)
new_mkVBalBranch3MkVBalBranch143(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Succ(ywv28290), Zero, dg) → new_mkVBalBranch3MkVBalBranch144(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, dg)
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Zero), bc, bd) → new_mkBalBranch6MkBalBranch51(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_primPlusInt(ywv22140, Neg(ywv22290)) → new_primMinusNat0(ywv22140, ywv22290)
new_splitGT25(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, Succ(ywv2170), Succ(ywv2180), eb) → new_splitGT25(ywv211, ywv212, ywv213, ywv214, ywv215, ywv216, ywv2170, ywv2180, eb)
new_addToFM_C11(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, be) → Branch(Pos(Succ(ywv1827)), new_addToFM0(ywv1823, ywv1828, be), ywv1824, ywv1825, ywv1826)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Pos(Succ(ywv295400)), Neg(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch118(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, new_primMulNat3(ywv29550), bc, bd)
new_mkBalBranch6MkBalBranch314(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, ywv2935, bc, bd) → new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitGT14(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Zero, Zero, dh) → new_splitGT15(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, dh)
new_mkVBalBranch3MkVBalBranch145(ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ywv2784, ywv2785, ywv2786, ywv2787, ywv2788, ywv2789, ywv2790, ea) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv2789), ywv2790, Branch(ywv2784, ywv2785, Pos(Succ(ywv2786)), ywv2787, ywv2788), Branch(ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783), ty_Int, ea)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Succ(ywv8200)), ywv83, ywv84), h) → new_mkVBalBranch3MkVBalBranch136(ywv80, ywv81, ywv8200, ywv83, ywv84, ywv330, ywv331, ywv333, ywv334, Succ(ywv3000), ywv31, new_primMulNat2(ywv8200), h)
new_addToFM_C4(Branch(Pos(Succ(ywv34000)), ywv341, ywv342, ywv343, ywv344), Succ(ywv3000), ywv31, h) → new_addToFM_C26(ywv34000, ywv341, ywv342, ywv343, ywv344, ywv3000, ywv31, ywv3000, ywv34000, h)
new_mkVBalBranch3MkVBalBranch142(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), ty_Int, h)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Neg(Succ(ywv295400)), Pos(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch1111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, new_primMulNat3(ywv29550), bc, bd)
new_splitLT13(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Succ(ywv6340), Zero, ef) → new_mkVBalBranch4(Succ(ywv628), ywv629, ywv631, new_splitLT7(ywv632, ywv633, ef), ef)
new_mkBalBranch6MkBalBranch1110(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch235(ywv110, ywv111, Zero, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, ywv704, h) → new_mkBalBranch(ywv110, ywv111, new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334, ywv113, h), ywv114, ty_Int, h)
new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2930000), Succ(ywv293400), bc, bd) → new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, ywv2930000, ywv293400, bc, bd)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Neg(Zero), Pos(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch0110(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, new_primMulNat3(ywv29330), bc, bd)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Neg(Succ(ywv33200)), ywv333, ywv334), Branch(ywv80, ywv81, ywv82, ywv83, ywv84), h) → new_mkVBalBranch3MkVBalBranch234(ywv80, ywv81, ywv82, ywv83, ywv84, ywv330, ywv331, ywv33200, ywv333, ywv334, Succ(ywv3000), ywv31, new_primPlusNat0(Succ(new_primPlusNat0(Succ(new_primPlusNat0(ywv33200, ywv33200)), ywv33200)), ywv33200), h)
new_mkVBalBranch3MkVBalBranch131(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb) → new_mkBalBranch(ywv2047, ywv2048, ywv2050, new_mkVBalBranch7(ywv2052, ywv2053, ywv2051, ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, bb), ty_Int, bb)
new_emptyFM(h) → EmptyFM
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Pos(Succ(ywv33200)), ywv333, ywv334, ywv110, ywv111, ywv112, ywv113, ywv114, h) → new_mkVBalBranch3MkVBalBranch239(ywv110, ywv111, ywv112, ywv113, ywv114, ywv330, ywv331, ywv33200, ywv333, ywv334, ywv300, ywv31, new_primMulNat0(ywv33200), h)
new_mkBalBranch6MkBalBranch411(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29280), bc, bd) → new_mkBalBranch6MkBalBranch413(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch116(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, Branch(ywv285140, ywv285141, ywv285142, ywv285143, ywv285144), ywv254334, bc, bd) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))), ywv285140, ywv285141, new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))), ywv28510, ywv28511, ywv28513, ywv285143, bc, bd), new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero))))))))))), ywv254330, ywv254331, ywv285144, ywv254334, bc, bd), bc, bd)
new_splitLT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → ywv33
new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, Zero, Zero, bc, bd) → new_mkBalBranch6MkBalBranch45(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT8(EmptyFM, h) → new_emptyFM(h)
new_mkVBalBranch3MkVBalBranch232(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Succ(ywv20550), bb) → new_mkBalBranch(ywv2042, ywv2043, new_mkVBalBranch2(ywv2052, ywv2053, ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051, ywv2045, bb), ywv2046, ty_Int, bb)
new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd) → new_mkBalBranch6MkBalBranch017(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_splitLT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_mkVBalBranch6(ywv3000, ywv31, ywv33, new_splitLT9(ywv34, h), h)
new_mkVBalBranch5(ywv31, Branch(ywv100, ywv101, ywv102, ywv103, ywv104), Branch(ywv340, ywv341, ywv342, ywv343, ywv344), h) → new_mkVBalBranch30(Zero, ywv31, ywv100, ywv101, ywv102, ywv103, ywv104, ywv340, ywv341, ywv342, ywv343, ywv344, h)
new_mkBalBranch6MkBalBranch41(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, Zero, bc, bd) → new_mkBalBranch6MkBalBranch44(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT13(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, Zero, Succ(ywv6350), ef) → new_splitLT14(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ef)
new_splitGT30(Pos(Zero), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → ywv34
new_splitGT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT25(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv4000, ywv3000, h)
new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, Zero, Succ(ywv293400), bc, bd) → new_mkBalBranch6MkBalBranch35(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch315(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv2954000), Zero, bc, bd) → new_mkBalBranch6MkBalBranch113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch135(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Pos(Succ(ywv217800)), bb) → new_mkVBalBranch3MkVBalBranch131(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkVBalBranch3MkVBalBranch227(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, Succ(ywv18540), Succ(ywv18550), da) → new_mkVBalBranch3MkVBalBranch227(ywv1843, ywv1844, ywv1845, ywv1846, ywv1847, ywv1848, ywv1849, ywv1850, ywv1851, ywv1852, ywv1853, ywv18540, ywv18550, da)
new_mkBalBranch6MkBalBranch30(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_mkBranch(Succ(Zero), ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Zero, Zero, bb) → new_mkVBalBranch3MkVBalBranch132(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_addToFM_C4(Branch(Neg(Zero), ywv341, ywv342, ywv343, ywv344), Zero, ywv31, h) → Branch(Pos(Zero), new_addToFM0(ywv341, ywv31, h), ywv342, ywv343, ywv344)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Zero), ywv113, ywv114, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Pos(Zero), ywv113, ywv114), ty_Int, h)
new_mkBalBranch6MkBalBranch110(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv2956, bc, bd) → new_mkBalBranch6MkBalBranch111(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, ywv2956, bc, bd)
new_mkBalBranch6MkBalBranch50(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(Succ(Zero))), bc, bd) → new_mkBalBranch6MkBalBranch5(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch019(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Pos(Succ(ywv293200)), Pos(ywv29330), bc, bd) → new_mkBalBranch6MkBalBranch013(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv293200, new_primMulNat3(ywv29330), bc, bd)
new_splitGT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_mkVBalBranch4(Succ(ywv3000), ywv31, new_splitGT8(ywv33, h), ywv34, h)
new_mkVBalBranch3MkVBalBranch228(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, db) → new_mkVBalBranch3MkVBalBranch139(ywv1319, ywv1320, ywv1321, ywv1322, ywv1323, ywv1324, ywv1325, ywv1326, ywv1327, ywv1328, ywv1329, db)
new_splitGT15(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, dh) → ywv586
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Succ(ywv8200)), ywv83, ywv84), h) → new_mkBalBranch(ywv80, ywv81, new_mkVBalBranch2(Succ(ywv3000), ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv83, h), ywv84, ty_Int, h)
new_primMinusNat0(Zero, Succ(ywv542000)) → Neg(Succ(ywv542000))
new_splitGT30(Neg(ywv300), ywv31, ywv32, ywv33, ywv34, Pos(Succ(ywv4000)), h) → new_splitGT6(ywv34, ywv4000, h)
new_mkVBalBranch3MkVBalBranch134(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Pos(ywv21770), bb) → new_mkVBalBranch3MkVBalBranch131(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkVBalBranch3MkVBalBranch233(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkBalBranch(ywv264, ywv265, ywv267, new_mkVBalBranch8(ywv269, ywv270, ywv268, ywv259, ywv260, ywv262, ywv263, cb), ty_Int, cb)
new_mkVBalBranch3MkVBalBranch240(ywv259, ywv260, Succ(ywv26100), ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkVBalBranch3MkVBalBranch146(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, new_primPlusNat0(new_primMulNat0(ywv26100), Succ(ywv26100)), cb)
new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv2177000), Succ(ywv215000), bb) → new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv2177000, ywv215000, bb)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Zero), ywv113, ywv114, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Neg(Zero), ywv113, ywv114), ty_Int, h)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Zero), ywv113, ywv114, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Pos(Zero), ywv113, ywv114), ty_Int, h)
new_mkBalBranch6MkBalBranch36(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv2930000), Zero, bc, bd) → new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Zero), Neg(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch43(ywv254330, ywv254331, ywv2851, ywv254334, new_primMulNat(ywv29200), bc, bd)
new_mkBalBranch6MkBalBranch415(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29270), ywv292100, bc, bd) → new_mkBalBranch6MkBalBranch416(ywv254330, ywv254331, ywv2851, ywv254334, ywv29270, ywv292100, bc, bd)
new_splitLT7(Branch(ywv340, ywv341, ywv342, ywv343, ywv344), ywv4000, h) → new_splitLT30(ywv340, ywv341, ywv342, ywv343, ywv344, Pos(Succ(ywv4000)), h)
new_splitGT13(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, Succ(ywv6250), Zero, cc) → new_splitGT12(ywv619, ywv620, ywv621, ywv622, ywv623, ywv624, cc)
new_mkVBalBranch3MkVBalBranch135(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Neg(Succ(ywv217800)), bb) → new_mkVBalBranch3MkVBalBranch130(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_splitLT30(Pos(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → new_splitLT9(ywv33, h)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Zero), ywv83, ywv84), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(ywv3000)), ywv31, Branch(ywv330, ywv331, Neg(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Pos(Zero), ywv83, ywv84), ty_Int, h)
new_mkVBalBranch6(ywv3000, ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Zero), ywv83, ywv84), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(Succ(ywv3000)), ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv80, ywv81, Neg(Zero), ywv83, ywv84), ty_Int, h)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Pos(Succ(ywv295400)), Pos(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch110(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv295400, new_primMulNat3(ywv29550), bc, bd)
new_splitLT14(ywv628, ywv629, ywv630, ywv631, ywv632, ywv633, ef) → ywv631
new_mkBalBranch6MkBalBranch46(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(ywv292100)), Pos(ywv29200), bc, bd) → new_mkBalBranch6MkBalBranch40(ywv254330, ywv254331, ywv2851, ywv254334, ywv292100, new_primMulNat(ywv29200), bc, bd)
new_mkVBalBranch3MkVBalBranch237(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Zero, de) → new_mkVBalBranch3MkVBalBranch238(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, de)
new_mkVBalBranch3MkVBalBranch143(ywv2817, ywv2818, ywv2819, ywv2820, ywv2821, ywv2822, ywv2823, ywv2824, ywv2825, ywv2826, ywv2827, ywv2828, Zero, Succ(ywv28300), dg) → new_mkBalBranch(ywv2822, ywv2823, ywv2825, new_mkVBalBranch4(ywv2827, ywv2828, ywv2826, Branch(ywv2817, ywv2818, Neg(Succ(ywv2819)), ywv2820, ywv2821), dg), ty_Int, dg)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Succ(ywv34200)), ywv343, ywv344), h) → new_mkBalBranch(ywv340, ywv341, new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), ywv343, h), ywv344, ty_Int, h)
new_mkBalBranch6MkBalBranch013(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv293200, Succ(ywv29500), bc, bd) → new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv293200, ywv29500, bc, bd)
new_mkVBalBranch3MkVBalBranch221(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, bg) → new_mkVBalBranch3MkVBalBranch137(ywv1304, ywv1305, ywv1306, ywv1307, ywv1308, ywv1309, ywv1310, ywv1311, ywv1312, ywv1313, ywv1314, ywv1315, new_primMulNat2(ywv1306), bg)
new_addToFM_C25(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, Zero, Zero, cf) → new_addToFM_C24(ywv1222, ywv1223, ywv1224, ywv1225, ywv1226, ywv1227, ywv1228, cf)
new_mkVBalBranch3MkVBalBranch126(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv93, ywv94, ywv300, ywv31, Succ(ywv6140), h) → new_mkBalBranch(ywv90, ywv91, ywv93, new_mkVBalBranch4(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Neg(Succ(ywv34200)), ywv343, ywv344), h), ty_Int, h)
new_mkVBalBranch9(ywv2789, ywv2790, Branch(ywv27880, ywv27881, ywv27882, ywv27883, ywv27884), ywv2779, ywv2780, ywv2781, ywv2782, ywv2783, ea) → new_mkVBalBranch30(ywv2789, ywv2790, ywv27880, ywv27881, ywv27882, ywv27883, ywv27884, ywv2779, ywv2780, Pos(Succ(ywv2781)), ywv2782, ywv2783, ea)
new_primPlusInt0(Pos(ywv28550), ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_primPlusInt(ywv28550, new_sizeFM(ywv254334, bc, bd))
new_mkVBalBranch3MkVBalBranch127(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Zero, Succ(ywv28150), bf) → new_mkBalBranch(ywv2807, ywv2808, ywv2810, new_mkVBalBranch4(ywv2812, ywv2813, ywv2811, Branch(ywv2802, ywv2803, Pos(Succ(ywv2804)), ywv2805, ywv2806), bf), ty_Int, bf)
new_primPlusNat0(Succ(ywv3540), Succ(ywv62000000)) → Succ(Succ(new_primPlusNat0(ywv3540, ywv62000000)))
new_mkBalBranch6MkBalBranch31(ywv254330, ywv254331, ywv2851, ywv254334, Zero, bc, bd) → new_mkBalBranch6MkBalBranch33(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv110, ywv111, Pos(Succ(ywv11200)), ywv113, ywv114, h) → new_mkBalBranch(ywv110, ywv111, new_mkVBalBranch2(ywv300, ywv31, ywv330, ywv331, Pos(Zero), ywv333, ywv334, ywv113, h), ywv114, ty_Int, h)
new_splitGT23(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Zero, bh) → new_splitGT5(ywv224, ywv225, bh)
new_splitGT23(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, Succ(ywv2260), Succ(ywv2270), bh) → new_splitGT23(ywv220, ywv221, ywv222, ywv223, ywv224, ywv225, ywv2260, ywv2270, bh)
new_splitGT30(Neg(Zero), ywv31, ywv32, ywv33, ywv34, Neg(Zero), h) → ywv34
new_mkVBalBranch3MkVBalBranch146(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, Succ(ywv7740), cb) → new_mkVBalBranch3MkVBalBranch147(ywv259, ywv260, ywv26100, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkVBalBranch3MkVBalBranch226(ywv259, ywv260, ywv261000, ywv262, ywv263, ywv264, ywv265, ywv267, ywv268, ywv269, ywv270, cb) → new_mkBalBranch(ywv259, ywv260, new_mkVBalBranch2(ywv269, ywv270, ywv264, ywv265, Pos(Succ(Zero)), ywv267, ywv268, ywv262, cb), ywv263, ty_Int, cb)
new_mkVBalBranch3MkVBalBranch127(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, Succ(ywv28140), Zero, bf) → new_mkVBalBranch3MkVBalBranch123(ywv2802, ywv2803, ywv2804, ywv2805, ywv2806, ywv2807, ywv2808, ywv2809, ywv2810, ywv2811, ywv2812, ywv2813, bf)
new_mkBalBranch6MkBalBranch37(ywv254330, ywv254331, Branch(ywv28510, ywv28511, ywv28512, ywv28513, ywv28514), ywv254334, bc, bd) → new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, new_sizeFM(ywv28514, bc, bd), new_sizeFM(ywv28513, bc, bd), bc, bd)
new_mkBalBranch6MkBalBranch310(ywv254330, ywv254331, ywv2851, ywv254334, Zero, ywv293000, bc, bd) → new_mkBalBranch6MkBalBranch35(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_splitLT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Neg(Succ(ywv4000)), h) → new_splitLT25(ywv3000, ywv31, ywv32, ywv33, ywv34, ywv4000, ywv3000, ywv4000, h)
new_primMulNat3(Succ(ywv293300)) → new_primPlusNat0(new_primMulNat1(ywv293300), Succ(ywv293300))
new_mkBalBranch6MkBalBranch0111(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Zero, bc, bd) → new_mkBalBranch6MkBalBranch012(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkVBalBranch3MkVBalBranch128(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Zero, cd) → new_mkVBalBranch3MkVBalBranch143(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Zero, cd)
new_mkVBalBranch3MkVBalBranch222(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkVBalBranch3MkVBalBranch223(ywv259, ywv260, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb)
new_mkBalBranch6MkBalBranch31(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29410), bc, bd) → new_mkBalBranch6MkBalBranch32(ywv254330, ywv254331, ywv2851, ywv254334, ywv29410, Zero, bc, bd)
new_mkVBalBranch7(ywv300, ywv31, Branch(ywv3340, ywv3341, ywv3342, ywv3343, ywv3344), ywv110, ywv111, ywv11200, ywv113, ywv114, h) → new_mkVBalBranch30(ywv300, ywv31, ywv3340, ywv3341, ywv3342, ywv3343, ywv3344, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, h)
new_mkVBalBranch3MkVBalBranch230(ywv340, ywv341, Zero, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkBalBranch(ywv90, ywv91, ywv93, new_mkVBalBranch4(ywv300, ywv31, ywv94, Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h), ty_Int, h)
new_mkVBalBranch3MkVBalBranch122(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv2052), ywv2053, Branch(ywv2047, ywv2048, Neg(Succ(ywv2049)), ywv2050, ywv2051), Branch(ywv2042, ywv2043, Neg(Succ(ywv2044)), ywv2045, ywv2046), ty_Int, bb)
new_mkVBalBranch3MkVBalBranch128(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv20380), cd) → new_mkVBalBranch3MkVBalBranch143(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv1957), Succ(ywv20380), cd)
new_mkVBalBranch30(ywv300, ywv31, ywv330, ywv331, Neg(Zero), ywv333, ywv334, ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114, h) → new_mkVBalBranch3MkVBalBranch141(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, new_primMulNat2(ywv11200), h)
new_mkBalBranch6MkBalBranch1115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv29610), ywv295400, bc, bd) → new_mkBalBranch6MkBalBranch112(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, ywv29610, ywv295400, bc, bd)
new_splitLT30(Neg(Succ(ywv3000)), ywv31, ywv32, ywv33, ywv34, Pos(Zero), h) → new_mkVBalBranch6(ywv3000, ywv31, ywv33, new_splitLT8(ywv34, h), h)
new_mkVBalBranch3MkVBalBranch129(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, Succ(ywv2177000), Zero, bb) → new_mkVBalBranch3MkVBalBranch130(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_mkBalBranch6MkBalBranch0111(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv29480), bc, bd) → new_mkBalBranch6MkBalBranch013(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv29480, Zero, bc, bd)
new_mkBalBranch6MkBalBranch1113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Succ(ywv29620), bc, bd) → new_mkBalBranch6MkBalBranch114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch38(ywv254330, ywv254331, ywv2851, ywv254334, Succ(ywv29400), bc, bd) → new_mkBalBranch6MkBalBranch35(ywv254330, ywv254331, ywv2851, ywv254334, bc, bd)
new_mkVBalBranch3MkVBalBranch240(ywv259, ywv260, Zero, ywv262, ywv263, ywv264, ywv265, ywv266, ywv267, ywv268, ywv269, ywv270, cb) → new_mkBalBranch(ywv264, ywv265, ywv267, new_mkVBalBranch10(ywv269, ywv270, ywv268, ywv259, ywv260, ywv262, ywv263, cb), ty_Int, cb)
new_mkVBalBranch3MkVBalBranch237(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, Succ(ywv19470), Succ(ywv19480), de) → new_mkVBalBranch3MkVBalBranch237(ywv1935, ywv1936, ywv1937, ywv1938, ywv1939, ywv1940, ywv1941, ywv1942, ywv1943, ywv1944, ywv1945, ywv1946, ywv19470, ywv19480, de)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Pos(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Neg(Zero), ywv343, ywv344), ty_Int, h)
new_mkVBalBranch4(ywv300, ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Pos(ywv300), ywv31, Branch(ywv90, ywv91, Neg(Zero), ywv93, ywv94), Branch(ywv340, ywv341, Pos(Zero), ywv343, ywv344), ty_Int, h)
new_mkBalBranch6MkBalBranch011(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv29520), ywv293200, bc, bd) → new_mkBalBranch6MkBalBranch014(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, ywv29520, ywv293200, bc, bd)
new_primPlusInt0(Neg(ywv28550), ywv254330, ywv254331, ywv2851, ywv254334, bc, bd) → new_primPlusInt1(ywv28550, new_sizeFM(ywv254334, bc, bd))
new_mkVBalBranch3MkVBalBranch236(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, Succ(ywv19620), Succ(ywv19630), cd) → new_mkVBalBranch3MkVBalBranch236(ywv1950, ywv1951, ywv1952, ywv1953, ywv1954, ywv1955, ywv1956, ywv1957, ywv1958, ywv1959, ywv1960, ywv1961, ywv19620, ywv19630, cd)
new_mkBalBranch6MkBalBranch016(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, Succ(ywv29440), bc, bd) → new_mkBalBranch6MkBalBranch015(ywv254330, ywv254331, ywv2851, ywv2543340, ywv2543341, ywv2543342, ywv2543343, ywv2543344, bc, bd)
new_mkVBalBranch3MkVBalBranch230(ywv340, ywv341, Succ(ywv34200), ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, ywv613, h) → new_mkVBalBranch3MkVBalBranch237(ywv340, ywv341, ywv34200, ywv343, ywv344, ywv90, ywv91, ywv9200, ywv93, ywv94, ywv300, ywv31, Succ(ywv613), ywv34200, h)
new_addToFM_C12(ywv1822, ywv1823, ywv1824, ywv1825, ywv1826, ywv1827, ywv1828, Succ(ywv18290), Zero, be) → new_mkBalBranch(Pos(Succ(ywv1822)), ywv1823, ywv1825, new_addToFM_C4(ywv1826, Succ(ywv1827), ywv1828, be), ty_Int, be)
new_mkVBalBranch3MkVBalBranch134(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, ywv21500, Neg(Zero), bb) → new_mkVBalBranch3MkVBalBranch131(ywv2042, ywv2043, ywv2044, ywv2045, ywv2046, ywv2047, ywv2048, ywv2049, ywv2050, ywv2051, ywv2052, ywv2053, bb)
new_addToFM_C4(EmptyFM, ywv300, ywv31, h) → Branch(Pos(ywv300), ywv31, Pos(Succ(Zero)), new_emptyFM(h), new_emptyFM(h))
new_mkVBalBranch3MkVBalBranch136(ywv110, ywv111, ywv11200, ywv113, ywv114, ywv330, ywv331, ywv333, ywv334, ywv300, ywv31, Zero, h) → new_mkBranch(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Succ(Zero)))))))))))), Neg(ywv300), ywv31, Branch(ywv330, ywv331, Pos(Zero), ywv333, ywv334), Branch(ywv110, ywv111, Neg(Succ(ywv11200)), ywv113, ywv114), ty_Int, h)
new_mkBalBranch6MkBalBranch1115(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Zero, ywv295400, bc, bd) → new_mkBalBranch6MkBalBranch114(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, bc, bd)
new_mkBalBranch6MkBalBranch34(ywv254330, ywv254331, ywv2851, ywv254334, Pos(Succ(ywv293000)), Pos(ywv29310), bc, bd) → new_mkBalBranch6MkBalBranch313(ywv254330, ywv254331, ywv2851, ywv254334, ywv293000, new_primMulNat(ywv29310), bc, bd)
new_splitGT14(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, Succ(ywv5880), Zero, dh) → new_splitGT15(ywv582, ywv583, ywv584, ywv585, ywv586, ywv587, dh)
new_mkBalBranch6MkBalBranch117(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, Neg(Zero), Pos(ywv29550), bc, bd) → new_mkBalBranch6MkBalBranch1113(ywv254330, ywv254331, ywv28510, ywv28511, ywv28512, ywv28513, ywv28514, ywv254334, new_primMulNat3(ywv29550), bc, bd)
new_primMinusNat0(Succ(ywv132000), Succ(ywv542000)) → new_primMinusNat0(ywv132000, ywv542000)
new_splitLT6(Branch(ywv330, ywv331, ywv332, ywv333, ywv334), ywv4000, h) → new_splitLT30(ywv330, ywv331, ywv332, ywv333, ywv334, Neg(Succ(ywv4000)), h)

The set Q consists of the following terms:

new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_addToFM(x0, x1, x2, x3)
new_splitGT14(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_splitGT6(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Zero)), x4, x5)
new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkBalBranch6MkBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMinusNat0(Zero, Zero)
new_splitLT30(Neg(x0), x1, x2, EmptyFM, x3, Pos(Succ(x4)), x5)
new_splitLT40(x0, x1)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Zero, x6, x7, x8, x9, Zero, x10)
new_mkVBalBranch3MkVBalBranch124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_addToFM_C3(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5)
new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5)
new_primMulNat3(Succ(x0))
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Pos(x13), x14)
new_splitLT9(Branch(x0, x1, x2, x3, x4), x5)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Neg(x9), x10, x11), x12)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Zero), x9, x10), x11)
new_splitLT23(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch226(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5)
new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5)
new_splitGT25(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_splitLT12(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_splitLT30(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), Branch(x8, x9, x10, x11, x12), Pos(Succ(x13)), x14)
new_mkBalBranch6MkBalBranch42(x0, x1, x2, x3, x4, x5)
new_splitLT8(Branch(x0, x1, x2, x3, x4), x5)
new_mkVBalBranch3MkVBalBranch131(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitGT23(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12)
new_mkVBalBranch3MkVBalBranch147(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_splitLT24(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch10(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11)
new_splitGT5(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_splitLT25(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6Size_l(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch230(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_primMinusNat0(Succ(x0), Succ(x1))
new_addToFM_C3(Branch(Pos(x0), x1, x2, x3, x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch125(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Succ(x5)), x6)
new_sizeFM(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT12(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch2(x0, x1, x2, x3, x4, x5, x6, Branch(x7, x8, x9, x10, x11), x12)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_splitGT25(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch225(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch(x0, x1, x2, x3, x4, x5)
new_primPlusNat0(Zero, Succ(x0))
new_mkVBalBranch10(x0, x1, EmptyFM, x2, x3, x4, x5, x6)
new_splitLT26(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch35(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch114(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), Zero, x12)
new_addToFM_C3(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6)
new_splitGT13(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch015(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkBalBranch6MkBalBranch30(x0, x1, x2, x3, x4, x5)
new_splitGT7(Branch(x0, x1, x2, x3, x4), x5)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch124(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_splitGT30(Neg(Zero), x0, x1, x2, x3, Neg(Zero), x4)
new_splitGT23(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7)
new_splitLT13(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_primMulNat3(Zero)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_mkVBalBranch3MkVBalBranch139(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), Branch(x6, x7, x8, x9, x10), x11)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_splitLT6(EmptyFM, x0, x1)
new_splitGT5(EmptyFM, x0, x1)
new_mkVBalBranch3MkVBalBranch137(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_splitGT30(Neg(Zero), x0, x1, x2, x3, Neg(Succ(x4)), x5)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(Succ(x13)), x14)
new_mkBranch(x0, x1, x2, x3, x4, x5, x6)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_primMulNat(Zero)
new_splitLT7(EmptyFM, x0, x1)
new_mkBalBranch6MkBalBranch48(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, x10, Succ(Succ(x11)), x12)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkBalBranch6MkBalBranch311(x0, x1, x2, x3, x4, x5, x6, x7)
new_sizeFM(Branch(x0, x1, x2, x3, x4), x5, x6)
new_splitLT25(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Zero), x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkVBalBranch40(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_splitGT14(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_splitLT13(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_splitLT30(Neg(Zero), x0, x1, x2, x3, Neg(Zero), x4)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkVBalBranch3MkVBalBranch231(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch145(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_splitLT30(Pos(Zero), x0, x1, x2, x3, Pos(Zero), x4)
new_splitGT25(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch8(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11)
new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5)
new_splitLT13(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch234(x0, x1, Pos(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, Pos(x9), x10, x11), x12)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_primPlusNat0(Succ(x0), Zero)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch37(x0, x1, EmptyFM, x2, x3, x4)
new_splitLT13(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch0111(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch1110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5)
new_splitLT25(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_splitLT30(Pos(Zero), x0, x1, x2, x3, Pos(Succ(x4)), x5)
new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, Succ(x6), x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_addToFM0(x0, x1, x2)
new_splitGT12(x0, x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkVBalBranch3MkVBalBranch222(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_addToFM2(x0, x1, x2, x3)
new_mkVBalBranch3MkVBalBranch223(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_primPlusNat0(Zero, Zero)
new_mkBalBranch6MkBalBranch313(x0, x1, x2, x3, x4, x5, x6, x7)
new_addToFM_C14(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch30(x0, x1, x2, x3, Neg(Succ(x4)), x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch118(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch49(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch410(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkVBalBranch9(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7)
new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Succ(x5)), x6)
new_mkVBalBranch3MkVBalBranch136(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch149(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch4(x0, x1, EmptyFM, x2, x3)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, Succ(Zero), x12)
new_addToFM_C4(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5)
new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, x10, Succ(Zero), x11)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch1112(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch37(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9)
new_splitGT26(x0, x1, x2, x3, x4, x5, x6)
new_splitGT30(Neg(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5)
new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Neg(Zero), x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch128(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch018(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_mkVBalBranch8(x0, x1, EmptyFM, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch5(x0, x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch122(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch113(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_addToFM1(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT25(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_splitLT8(EmptyFM, x0)
new_mkBalBranch6MkBalBranch310(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6MkBalBranch016(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch111(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_addToFM_C13(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_addToFM_C3(EmptyFM, x0, x1, x2)
new_addToFM_C11(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitGT13(x0, x1, x2, x3, x4, x5, Succ(x6), Zero, x7)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkVBalBranch7(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, Succ(Succ(x12)), x13)
new_splitGT14(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch130(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_primPlusInt(x0, Neg(x1))
new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Pos(Succ(x8)), x9, x10, x11)
new_mkBalBranch6MkBalBranch115(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT12(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Zero, x7, x8, x9, x10, Zero, x11)
new_mkVBalBranch3MkVBalBranch141(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch138(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch5(x0, EmptyFM, x1, x2)
new_mkBalBranch6MkBalBranch110(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Zero, x4, x5)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Zero))), x4, x5)
new_addToFM_C4(Branch(Pos(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch229(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch128(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_primMinusNat0(Zero, Succ(x0))
new_mkVBalBranch3MkVBalBranch235(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Pos(Zero), Pos(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Succ(x12)), x13)
new_mkVBalBranch30(x0, x1, x2, x3, Pos(Succ(x4)), x5, x6, x7, x8, x9, x10, x11, x12)
new_splitLT23(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Zero, x11)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Succ(x12)), x13)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Succ(x8), x9)
new_mkVBalBranch3MkVBalBranch134(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, Neg(Zero), x13)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Neg(Zero), x12)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Succ(x4), x5, x6, x7)
new_mkBalBranch6MkBalBranch011(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_splitGT30(Pos(Zero), x0, x1, x2, x3, Pos(Zero), x4)
new_addToFM_C4(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch133(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_mkBalBranch6Size_r(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch132(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch142(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Zero, x8, x9)
new_mkBalBranch6MkBalBranch47(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulNat(Succ(x0))
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch314(x0, x1, x2, x3, x4, x5, x6, x7)
new_primMulNat0(x0)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_primMulNat1(x0)
new_mkBalBranch6MkBalBranch1111(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Zero)), x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), x13)
new_primPlusInt0(Pos(x0), x1, x2, x3, x4, x5, x6)
new_mkVBalBranch3MkVBalBranch221(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Zero), x4, x5)
new_mkVBalBranch3MkVBalBranch146(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_splitGT30(Neg(Zero), x0, x1, x2, x3, Pos(Zero), x4)
new_splitGT30(Pos(Zero), x0, x1, x2, x3, Neg(Zero), x4)
new_splitLT12(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch7(x0, x1, EmptyFM, x2, x3, x4, x5, x6, x7)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_splitLT30(Neg(x0), x1, x2, Branch(x3, x4, x5, x6, x7), EmptyFM, Pos(Succ(x8)), x9)
new_mkBalBranch6MkBalBranch010(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch233(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Succ(x9), x10, x11)
new_mkBalBranch6MkBalBranch1113(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch2(x0, x1, x2, x3, x4, x5, x6, EmptyFM, x7)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Succ(x4)), x5, x6), Branch(x7, x8, x9, x10, x11), x12)
new_splitGT8(Branch(x0, x1, x2, x3, x4), x5)
new_addToFM_C23(x0, x1, x2, x3, x4, x5, x6, x7)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch240(x0, x1, Succ(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch33(x0, x1, x2, x3, x4, x5)
new_splitGT30(Pos(x0), x1, x2, x3, x4, Neg(Succ(x5)), x6)
new_splitGT30(Neg(x0), x1, x2, x3, x4, Pos(Succ(x5)), x6)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Zero), Pos(x8), x9, x10)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Neg(x8), x9, x10)
new_mkBalBranch6MkBalBranch014(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), Zero, x9, x10)
new_splitGT8(EmptyFM, x0)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, EmptyFM, x3, x4)
new_mkVBalBranch3MkVBalBranch126(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Succ(x11), x12)
new_primMinusNat0(Succ(x0), Zero)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_splitLT23(x0, x1, x2, x3, x4, x5, Zero, Zero, x6)
new_mkVBalBranch6(x0, x1, EmptyFM, x2, x3)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, Succ(x7), Zero, x8)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Neg(Zero), x8, x9), x10)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Neg(Zero), x4, x5)
new_splitLT30(Neg(Succ(x0)), x1, x2, x3, x4, Neg(Succ(x5)), x6)
new_addToFM_C4(Branch(Neg(x0), x1, x2, x3, x4), Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Pos(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Neg(Succ(x4)), Pos(x5), x6, x7)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Succ(x8)), x9, x10), x11)
new_addToFM_C26(x0, x1, x2, x3, x4, x5, x6, Zero, Succ(x7), x8)
new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Succ(x8)), x9, x10, x11)
new_mkBalBranch6MkBalBranch412(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkVBalBranch3MkVBalBranch239(x0, x1, Pos(Succ(Succ(x2))), x3, x4, x5, x6, Succ(x7), x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch1114(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Neg(Zero), x4, x5), Branch(x6, x7, Neg(Succ(x8)), x9, x10), x11)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Zero, Zero, x4, x5)
new_splitLT30(Pos(x0), x1, x2, x3, x4, Neg(Succ(x5)), x6)
new_splitGT7(EmptyFM, x0)
new_addToFM_C4(EmptyFM, x0, x1, x2)
new_primPlusInt1(x0, Neg(x1))
new_splitGT25(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch30(x0, x1, x2, x3, Pos(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10)
new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Pos(Zero), x8, x9, x10)
new_mkVBalBranch9(x0, x1, Branch(x2, x3, x4, x5, x6), x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch234(x0, x1, Neg(x2), x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
new_splitLT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Succ(x5)), x6)
new_mkVBalBranch3MkVBalBranch135(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Pos(Zero), x12)
new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Succ(x4), x5, x6)
new_splitLT6(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch112(x0, x1, x2, x3, x4, x5, x6, x7, Zero, Succ(x8), x9, x10)
new_mkBalBranch6MkBalBranch119(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10)
new_mkVBalBranch3MkVBalBranch150(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, Pos(Zero), x4, x5), Branch(x6, x7, Pos(Zero), x8, x9), x10)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Neg(Succ(x4)), Neg(x5), x6, x7)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Zero, x9, x10)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9, x10)
new_mkBalBranch6MkBalBranch116(x0, x1, x2, x3, x4, x5, EmptyFM, x6, x7, x8)
new_splitGT15(x0, x1, x2, x3, x4, x5, x6)
new_addToFM_C25(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_splitGT6(Branch(x0, x1, x2, x3, x4), x5, x6)
new_splitLT30(Neg(Zero), x0, x1, x2, x3, Neg(Succ(x4)), x5)
new_mkVBalBranch3MkVBalBranch235(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch41(x0, x1, x2, x3, x4, Zero, x5, x6)
new_mkBalBranch6MkBalBranch312(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitLT14(x0, x1, x2, x3, x4, x5, x6)
new_splitGT30(Pos(Succ(x0)), x1, x2, x3, x4, Pos(Zero), x5)
new_primMulNat2(x0)
new_splitLT9(EmptyFM, x0)
new_addToFM_C12(x0, x1, x2, x3, x4, x5, x6, Zero, Zero, x7)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Pos(x9), x10, x11)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch240(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_mkBalBranch6MkBalBranch415(x0, x1, x2, x3, Zero, x4, x5, x6)
new_mkBalBranch6MkBalBranch45(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch44(x0, x1, x2, Branch(x3, x4, x5, x6, x7), x8, x9)
new_mkBalBranch6MkBalBranch012(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
new_splitLT7(Branch(x0, x1, x2, x3, x4), x5, x6)
new_mkBalBranch6MkBalBranch39(x0, x1, x2, x3, x4, x5, x6, x7)
new_splitLT23(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_primPlusInt(x0, Pos(x1))
new_mkBalBranch6MkBalBranch414(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch0110(x0, x1, x2, x3, x4, x5, x6, x7, Zero, x8, x9)
new_emptyFM(x0)
new_mkVBalBranch3MkVBalBranch143(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch315(x0, x1, x2, x3, Succ(x4), x5, x6)
new_splitGT30(Pos(Zero), x0, x1, x2, x3, Pos(Succ(x4)), x5)
new_splitLT11(x0, x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Succ(x8)), Neg(x9), x10, x11)
new_mkBalBranch6MkBalBranch019(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Pos(x9), x10, x11)
new_mkVBalBranch6(x0, x1, Branch(x2, x3, x4, x5, x6), EmptyFM, x7)
new_mkVBalBranch5(x0, Branch(x1, x2, x3, x4, x5), EmptyFM, x6)
new_mkBalBranch6MkBalBranch1115(x0, x1, x2, x3, x4, x5, x6, x7, Succ(x8), x9, x10, x11)
new_mkVBalBranch3MkVBalBranch148(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, x11)
new_mkBalBranch6MkBalBranch50(x0, x1, x2, x3, Pos(Succ(Succ(Succ(x4)))), x5, x6)
new_mkBalBranch6MkBalBranch34(x0, x1, x2, x3, Neg(Zero), Neg(x4), x5, x6)
new_mkVBalBranch30(x0, x1, x2, x3, Neg(Zero), x4, x5, x6, x7, Neg(Zero), x8, x9, x10)
new_primPlusInt2(Neg(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch129(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Succ(x13), x14)
new_splitGT23(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_primPlusInt0(Neg(x0), x1, x2, x3, x4, x5, x6)
new_mkBalBranch6MkBalBranch416(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkVBalBranch3MkVBalBranch123(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch31(x0, x1, x2, x3, Zero, x4, x5)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Pos(Zero), Neg(x4), x5, x6)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Neg(Zero), Pos(x4), x5, x6)
new_addToFM_C3(Branch(Neg(Zero), x0, x1, x2, x3), Zero, x4, x5)
new_primPlusNat0(Succ(x0), Succ(x1))
new_splitLT30(Neg(Zero), x0, x1, x2, x3, Pos(Zero), x4)
new_splitLT30(Pos(Zero), x0, x1, x2, x3, Neg(Zero), x4)
new_mkVBalBranch3MkVBalBranch127(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Succ(x12), Zero, x13)
new_mkVBalBranch3MkVBalBranch236(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkVBalBranch4(x0, x1, Branch(x2, x3, Pos(Succ(x4)), x5, x6), Branch(x7, x8, Neg(Succ(x9)), x10, x11), x12)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Zero, x12)
new_mkBalBranch6MkBalBranch411(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch228(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
new_addToFM_C4(Branch(Pos(Zero), x0, x1, x2, x3), Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch144(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch238(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_addToFM_C24(x0, x1, x2, x3, x4, x5, x6, x7)
new_addToFM_C3(Branch(Neg(Succ(x0)), x1, x2, x3, x4), Succ(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch230(x0, x1, Zero, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkVBalBranch3MkVBalBranch140(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, x12)
new_mkBalBranch6MkBalBranch43(x0, x1, x2, x3, Zero, x4, x5)
new_mkVBalBranch3MkVBalBranch227(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, Zero, Succ(x11), x12)
new_splitGT13(x0, x1, x2, x3, x4, x5, Zero, Succ(x6), x7)
new_mkBalBranch6MkBalBranch46(x0, x1, x2, x3, Pos(Succ(x4)), Pos(x5), x6, x7)
new_mkVBalBranch3MkVBalBranch220(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch013(x0, x1, x2, x3, x4, x5, x6, x7, x8, Succ(x9), x10, x11)
new_mkVBalBranch3MkVBalBranch232(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_mkBalBranch6MkBalBranch36(x0, x1, x2, x3, Succ(x4), Zero, x5, x6)
new_mkBalBranch6MkBalBranch38(x0, x1, x2, x3, Succ(x4), x5, x6)
new_mkVBalBranch3MkVBalBranch237(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, Zero, Succ(x12), x13)
new_splitGT13(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_splitGT14(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_mkBalBranch6MkBalBranch51(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch017(x0, x1, x2, x3, x4, x5, Branch(x6, x7, x8, x9, x10), x11, x12, x13)
new_splitGT23(x0, x1, x2, x3, x4, x5, Succ(x6), Succ(x7), x8)
new_primPlusInt2(Pos(x0), x1, x2, x3, x4, x5)
new_mkVBalBranch3MkVBalBranch224(x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Neg(Succ(x8)), Neg(x9), x10, x11)
new_primPlusInt1(x0, Pos(x1))
new_mkBalBranch6MkBalBranch413(x0, x1, x2, x3, x4, x5)
new_mkBalBranch6MkBalBranch32(x0, x1, x2, x3, x4, Succ(x5), x6, x7)
new_mkBalBranch6MkBalBranch117(x0, x1, x2, x3, x4, x5, x6, x7, Pos(Zero), Pos(x8), x9, x10)
new_splitGT24(x0, x1, x2, x3, 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: